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# 기탄수학 K4 답지 정답

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① 3x ②xy ③x, -x ④x2 , y3 ⑤ 2(x+y), 3, 3(x－y) ⑥ 2a ⑦ -4y ⑧ab ⑨a ⑩ -x ⑪ax2 ⑫ -4(x+y)⑬ -0.1x2 x ⑮ 6xy2 <풀이> ① 3×x=3x ②x×y=xy ③ 1×x=x, -1×x=-x ④x×x=x2, y×y×y=y3 ⑤ 2×(x+y)=2(x+y) (x-y)×3=3×(x-y)=3(x－y) ⑥ 2×a=2a ⑦y×(-4)=(-4)×y=-4y ⑧b×a=a×b=ab ⑨ 1×a=a ⑩x×(-1)=(-1)×x=-x ⑪x×a×x=a×x×x=ax2 ⑫ (x+y)×(-4)=(-4)×(x+y)=-4(x+y) ⑬x×(-0.1)×x=(-0.1)×x×x=-0.1x2 ⑭ 2×x× =2× ×x=1×x=x ⑮x×3×y×2×y=3×2×x×y×y=6xy2 1 2 1 2 <풀이> ① 2÷a= , b÷3= a÷b= , x÷y= ② (a+b)÷4= , 2÷(a-b)= ③a÷1= =a, a÷(-1)= =-a ④ = a, = a, - =-1a 2 a 2 2 3 2a 3 1 2 a 2 a -1 a 1 2 a-b a+b 4 x y a b b 3 2 a ① 5x＋y ② 3a-4b ③ -2(5-x)y ④ 1-2ab ⑤ 3ay+2x ⑥ 2ab-5x2y ⑦ (x-y)2 ⑧ (-a)3b ⑨ -(x-5)2 ⑩ (-x)3 (-y)2 ⑪x×y×z ⑫ 5×a×b ⑬ 4×x×x×y ⑭ -3×a×(-b)×(-b)×(-b) ⑮ -0.1×x×y×y � (x-y)×z � (x+y)×(x-y) � (a-b)×(a-b)×(a+b) � 3×a×b-2×a � -2×(x-1)×y×y×z ⑥b×2×a-y×5×x×x =2×a×b-5×x×x×y =2ab-5x2y ⑦ (x-y)×(x-y)=(x-y)2 ⑧ (-a)×(-a)×(-a)×b=(-a)3b ⑨ (x-5)×(x-5)×(-1)=(-1)×(x-5)×(x-5) =-(x-5)2 ⑩ (-x)×(-y)×(-y)×(-x)×(-x) =(-x)×(-x)×(-x)×(-y)×(-y) =(-x)3(-y)2 ⑪xyz=x×y×z ⑫ 5ab=5×a×b ⑬ 4x2y=4×x×x×y ⑭ -3a(-b)3=-3×a×(-b)×(-b)×(-b) ⑮ -0.1xy2 =-0.1×x×y×y � (x-y)z=(x-y)×z � (x+y)(x-y)=(x+y)×(x-y) � (a-b)2(a+b)=(a-b)×(a-b)×(a+b) � 3ab-2a=3×a×b-2×a � -2(x-1)y2z=-2×(x-1)×y×y×z ① , , , ② , ③a, -a ④ a, a, - a ⑤ ⑥ - ⑦ -⑧ ⑨ - ⑩ ⑪ - ⑫ ⑬ ⑭ -a-b a+b x+y x-y 3 a+b 5 x+y x-y 2 a b a x 1 x 3 a x 2 1 2 2 3 1 2 2 a-b a+b 4 x y a b b 3 2 a <풀이> ※ 덧셈 기호 ＋와 뺄셈 기호 －는 생략하면 안 된다. ① 5×x+y=5x＋y ② 3×a-4×b=3a-4b ③ (-2)×(5-x)×y=-2(5-x)y ④ 1-2×b×a=1-2×a×b=1-2ab ⑤ 3×y×a+2×x=3×a×y+2×x=3ay+2x

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## K-4

### 정답및풀이

⑤x÷2=x× = ⑥ (-3)÷a=(-3)× =-⑦ 1÷(-x)=1×&- *=-⑧a÷x=a× = ⑨a÷(-b)=a×&- *=-⑩ (x-y)÷2=(x-y)× = ⑪ (-5)÷(x+y)=(-5)× =-⑫ 3÷(a+b)=3× = ⑬ (x+y)÷(x-y)=(x+y)× = ⑭ -(a-b)÷(a+b)=-(a-b)× =-aa-b +b 1 a+b x+y x-y 1 x-y 3 a+b 1 a+b 5 x+y 1 x+y x-y 2 1 2 a b 1 b a x 1 x 1 x 1 x 3 a 1 a x 2 1 2 ① ② +y ③ -④ + ⑤ - ⑥ ⑦ -y- ⑧ - ⑨ -⑩ ⑪ 2÷x ⑫y÷4 ⑬ (a+b)÷3 ⑭ 1÷(x-y) ⑮ (b-1)÷(a+1) � 1÷x+y÷2 �a÷(-2) � (-3x)÷7 � (x+y)÷5 � (a+b)÷(-4) x (y+z)2 a 2 5 b x y 5 a a+b 2c 3 xy 2 y 4 x a 7b x 2 x yz <풀이> ※ 덧셈 기호 ＋와 뺄셈 기호 －는 생략하면 안 된다. ①x÷y÷z=x× × = ②x÷2+y=x× +y= +y ③ (-a)÷b÷7=(-a)× × =- a 7b 1 7 1 b x 2 1 2 x yz 1 z 1 y ④ 4÷x+2÷y=4× +2× = + ⑤ 3÷x÷(-y)=3× ×&- *=-⑥ (a+b)÷c÷2=(a+b)× × = ⑦ -y-5÷a=-y-5× =-y -⑧x÷y÷(-1)=x× ×(-1)=-⑨ 5÷b+a÷(-2)=5× +a×& *= -⑩x÷(y+z)÷(y+z)=x× × = = ⑪ =2÷x ⑫ =y÷4 ⑬ =(a+b)÷3 ⑭ =1÷(x-y) ⑮ =(b-1)÷(a+1) � + =1÷x+y÷2 � =a÷(-2) � =(-3x)÷7 � (x+y)= =(x+y)÷5 �a+b=(a+b)÷(-4) -4 x+y 5 1 5 -3x 7 a -2 y 2 1 x b-1 a+1 1 x-y a+b 3 y 4 2 x x (y+z)2 x (y+z)(y+z) 1 y+z 1 y+z a 2 5 b 1 2 1 b x y 1 y 5 a 1 a a+b 2c 1 2 1 c 3 xy 1 y 1 x 2 y 4 x 1 y 1 x ①z,z,y,y ②z,z,yz,yz,yz,z,z,xz,y,y,z,yz ③yz,z ④ × ⑤ ÷ ⑥ ×, × ⑦ +, × ⑧ ÷, - ⑨ ＋ ⑩ ×, × ⑪ ÷, ÷ ⑫ +, × ⑬ ÷,

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-<풀이> ①x×y÷z=x×y× = x÷y×z=x× ×z= ②x×(y÷z)=x× = x÷(y×z)=x÷yz=x× = x÷(y÷z)=x÷ =x× = (x÷y)÷z= ÷z= × = ③x÷yz= , xy÷z= ④x×y=xy ⑤ 4÷x= ⑥ 2×y×x=2×x×y=2xy ⑦x+y×z=x+yz ⑧x÷5-z= -z ⑨x＋x=2x ⑩y×y×y=y3 ⑪x÷y÷z=x× × = ⑫ (x+y)×2=2×(x+y)=2(x+y) ⑬x÷(y-z)= x y-z x yz 1 z 1 y x 5 4 x xy z x yz x yz 1 z x y x y xz y z y y z x yz 1 yz xy z y z xz y 1 y xy z 1 z ①abc ② ③ ④ ⑤ ⑥ 2x+3y ⑦ 2x- ⑧ +3y ⑨ -⑩ ⑪ - ⑫ ⑬ ⑭ ⑮ � � 3a- �a -� (x+y)- � -x+3y 4 2y z 3b 4 2b c 2xz y x2 y2 a2 b2 2x 3y 4x y 3a b 2y x+3 3 y 2 x 2 x 3 y ab cd a bc ac b ab c <풀이> ①a×b×c=abc ②a×b÷c=a×b× = ③a÷b×c=a× ×c= ④a÷b÷c=a× × = ⑤ab÷cd=ab× = ⑥ 2×x+3×y=2x+3y ⑦ 2×x-3÷y=2×x-3× =2x -⑧ 2÷x+3×y=2× +3×y= +3y ⑨ 2÷x-3÷y=2× -3× = -⑩ 2÷(x+3)×y＝2× ×y= ⑪a×(-3)÷b=a×(-3)× =-⑫x÷y×4=x× ×4= ⑬ ×x÷y= ×x× = ⑭a×a÷b÷b=a×a× × = ⑮x×x÷(y×y)=x×x÷y2 =x2× = � 2x÷y×z=2x× ×z= � 3a-2b÷c=3a-2b× =3a -�a-3b÷4=a-3b× =a -� (x+y)-2y÷z=(x+y)-2y× =(x+y )-�x÷(-4)+3×y=x×&- *+3×y =-x+3y 4 1 4 2y z 1 z 3b 4 1 4 2b c 1 c 2xz y 1 y x2 y2 1 y2 a2 b2 1 b 1 b 2x 3y 1 y 2 3 2 3 4x y 1 y 3a b 1 b 2y x+3 1 x+3 3 y 2 x 1 y 1 x 2 x 1 x 3 y 1 y ab cd 1 cd a bc 1 c 1 b ac b 1 b ab c 1 c

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## K-4

### 정답및풀이

① - +3y ② ③ ④a- ⑤ ⑥ ⑦ -5 ⑧ ⑨ +3x ⑩ - ⑪ -3(b+c) ⑫ -⑬ - ⑭ ⑮ -� +2(y-z) � - � -� -x+(y-z) � - +b d a c a b a b+c xy az 4 a 1 y 1 x a(b-2) cd 3x 1-y 3 xyz a 2 x yz xz y x+y z ac bd a 2b 2xy 3b 2x 5yz 2b c (a-3)x b 5z x+y a 2 <풀이> ①a÷(-2)+3×y=a×&- *+3×y=- +3y ② 5÷(x+y)×z=5× ×z= ③ (a-3)×x÷b=(a-3)×x× = ④a-2b÷c=a-2b× =a -⑤ 2x÷y÷5z=2x× × = ⑥ 2x×y÷3b=2x×y× = ⑦a÷2b-5=a× -5= -5 ⑧a÷b×c÷d=a× ×c× = ⑨ (x+y)÷z+3×x=(x+y)× +3×x = +3x ⑩ (x÷y)×z-x÷(y×z)=&x× *×z-x÷yz = ×z-x× = -⑪a÷2-(b+c)×3=a× -3×(b+c) =a-3(b+c) 2 1 2 x yz xz y 1 yz x y 1 y x+y z 1 z ac bd 1 d 1 b a 2b 1 2b 2xy 3b 1 3b 2x 5yz 1 5z 1 y 2b c 1 c (a-3)x b 1 b 5z x+y 1 x+y a 2 1 2 ⑫ (-3)÷xy÷z=(-3)× × =-⑬x÷(1-y)×(-3)=x× ×(-3)=-⑭a×(b-2)÷cd=a×(b-2)× = ⑮ (-1)÷x+1÷(-y)=(-1)× +1×&- * = -� 4÷a+(y-z)×2=4× +2×(y-z) = +2(y-z) �x×y÷(-a)÷z=x×y×&- *× =-�a×(-1)÷(b+c)=a×(-1)× =-� (-1)×x-(y-z)÷(-1) =(-1)×x-(y-z)×(-1) =-x+(y-z) �a÷b+(-a)÷c-b÷(-d) =a× +(-a)× -b×&- * = - +b d a c a b 1 d 1 c 1 b a b+c 1 b+c xy az 1 z 1 a 4 a 1 a 1 y 1 x 1 y 1 x a(b-2) cd 1 cd 3x 1-y 1 1-y 3 xyz 1 z 1 xy ①b÷a ②x×y÷z ③ 2×(a+b)÷(c+d) ④x÷(y×y)또는x÷y÷y ⑤ 3×(b-a)×(b-a) ⑥ (2×a+b)÷c ⑦x×y÷(x-y) ⑧c÷(a+b)+2×x ⑨x×y×z÷a ⑩ 5×a+(y-z)÷4 ⑪ 3×a÷b ⑫z÷(x×y) 또는z÷x÷y ⑬a×a÷(b×b) 또는a×a÷b÷b ⑭ 3×x×y÷(x-y) ⑮ (5-3×x)÷7 � (x-y)÷z-5×a � 5×a＋(a-3×b)÷4 �a÷(b×c×d) 또는a÷b÷c÷d � (x+y)÷{2×(x-y)} 또는 (x+y)÷2÷(x-y) � 3×(a-b)÷{4×(a+b)} 또는 3×(a-b)÷4÷(a+b)

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① am ② xt ③ cL ④ y시간 ⑤ b명 ⑥ xcm ⑦ 5bkg ⑧ amL ⑨ c분 ⑩ 100y원 ⑪ akm ⑫ bt ⑬ bcm2 ycm xm2 � aha � y초 � cg � 4bmm � 9 xcm3 200 1 8 1 20 3 10 13 125 1 40 9 20 3 100 9 10 1 500 1 4 1 25 3 20 1 125 1 50 3 10 1 20 <풀이> ① =b÷a ② =xy÷z=x×y÷z ③ =2(a+b)÷(c+d) =2×(a+b)÷(c+d) ④ =x÷y2=x÷(y×y) <다른 풀이> = =x× × =x÷y÷y ⑤ 3(b-a)2=3×(b-a)2=3×(b-a)×(b-a) ⑥ =(2a+b)÷c=(2×a+b)÷c ⑦ =xy÷(x-y)=x×y÷(x-y) ⑧ +2x=c÷(a+b)+2x=c÷(a+b)+2×x ⑨ =xyz÷a=x×y×z÷a ⑩ 5a+ =5×a+ =5×a+(y-z)÷4 ⑪ =3a÷b=3×a÷b ⑫ =z÷xy=z÷(x×y) <다른 풀이> = =z× × =z÷x÷y ⑬ =a2 ÷b2 =a×a÷(b×b) <다른 풀이> = =a×a× × =a×a÷b÷b ⑭ =3xy÷(x-y)=3×x×y÷(x-y) ⑮ =(5-3x)÷7=(5-3×x)÷7 � -5a=(x-y)÷z-5a=(x-y)÷z-5×a � 5a＋ =5×a＋ =5×a＋(a-3b)÷4 =5×a＋(a-3×b)÷4 � a =a÷(bcd)=a÷(b×c×d) bcd a-3b 4 a-3b 4 x-y z 5-3x 7 3xy x-y 1 b 1 b a×a b×b a2 b2 a2 b2 1 y 1 x z x×y z xy z xy 3a b y-z 4 y-z 4 xyz a c a+b xy x-y 2a+b c 1 y 1 y x y×y x y2 x y2 2(a+b) c+d xy z b a <다른 풀이> = =a× × × =a÷b÷c÷d � =(x+y)÷{2(x-y)} =(x+y)÷{2×(x-y)} <다른 풀이> = =(x+y)× × =(x+y)÷2÷(x-y) � =3(a-b)÷{4(a+b)} =3×(a-b)÷{4×(a+b)} <다른 풀이> = =3×(a-b)× × =3×(a-b)÷4÷(a+b) 1 a+b 1 4 3×(a-b) 4×(a+b) 3(a-b) 4(a+b) 3(a-b) 4(a+b) 1 x-y 1 2 x+y 2×(x-y) x+y 2(x-y) x+y 2(x-y) 1 d 1 c 1 b a b×c×d a bcd <풀이> ※a%= , a할= , a푼= , a리= ①a× = a(m) ②x× = x(t) ③c× =1c(L) 50 2 100 3 10 3 10 1 20 5 100 a 1000 a 100 a 10 a 100

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## K-4

### 정답및풀이

④y× = y(시간) ⑤b× = b(명) ⑥ 4× = x(cm) ⑦ 50× =5b(kg) ⑧ 25× = a(mL) ⑨ 2× = c(분) ⑩ 1000× =100y(원) ⑪a× = a(km) ⑫ 3× = b(t) ⑬b× = b(cm2) ⑭ 25× = y(cm) ⑮x× = x(m2) � 3× = a(ha) �y× = y(초) �c× = c(g) � 400× =4b(mm) �x× = 9 x(cm3) 200 45 1000 b 100 1 8 125 1000 1 20 5 100 3 10 a 10 13 125 104 1000 1 40 y 1000 9 20 45 100 3 100 b 100 9 10 9 10 y 10 1 500 c 1000 1 4 a 100 b 10 1 25 x 100 3 20 15 100 1 125 8 1000 ① 10xmm ② ycm ③ 1000akg ④ bt ⑤ 10000xcm2 ym2 ⑦ 60a초 ⑧ b분 ⑨ 100xa ⑩ 1 yha ⑪ (100x+y) cm 100 1 60 1 10000 1 1000 1 10 ⑫ &x+ y* m ⑬ (1000a+b) g ⑭ &a+ b* kg ⑮ (1000x+y) mL � &x+ y* L � (10a+b) mm � &a+ b* cm � (60x+y)분 � &x+1y*시간 60 1 10 1 1000 1 1000 1 100 <풀이> ①xcm=10×xmm=10xmm ②ymm= ×ycm= ycm ③at=1000×akg=1000akg ④bkg= ×bt= bt ⑤xm2 =10000×xcm2 =10000xcm2 ⑥ycm2= ×ym2= ym2 ⑦a분=60×a초=60a초 ⑧b초= ×b분= b분 ⑨xha=100×xa=100xa ⑩ya= ×yha= yha ⑪xmycm=(100×x+y) cm=(100x+y) cm ⑫xmycm=&x+ ×y* m=&x+ y* m ⑬akgbg=(1000×a+b) g=(1000a+b) g ⑭akgbg=&a+ ×b* kg=&a+ b* kg ⑮xLymL=(1000×x+y) mL =(1000x+y) mL �xLymL=&x+ ×y* L=&x+ y* L �acmbmm=(10×a+b) mm=(10a+b) mm �acmbmm=&a+ ×b* cm =&a+ b* cm �x시간y분=(60×x+y)분 =(60x+y)분 �x시간y분=&x+ ×y*시간 =&x+1y*시간 60 1 60 1 10 1 10 1 1000 1 1000 1 1000 1 1000 1 100 1 100 1 100 1 100 1 60 1 60 1 10000 1 10000 1 1000 1 1000 1 10 1 10

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① 2, 5 ② -3 ③ 2, 4 ④ 8 ⑤ 2, -3 ⑥ 14 ⑦ 2, 1 ⑧ -⑨ 2, -4 ⑩ 0 ⑪ , 1 ⑫ -3 ⑬ , 2 ⑭ -3 ⑮ , -4 � 10 � 5, � 10 � , � -1 6 3 4 1 2 1 10 1 2 1 2 1 2 1 2 1 2 1 2 <풀이> ※ 문자에 주어진 수를 대입하고 계산한다. 문 자에 수를 대입하여 계산할 때에는 숫자와 문 자 사이에 생략되었던 곱셈 기호를 되살려야 한다. ①a+3=2+3=5 ②a-5=2-5=-3 ③ 2a=2×2=4 ④ 4a=4×2=8 ⑤ 3a-9=3×2-9=6-9=-3 ⑥ 5a+4=5×2+4=10+4=14 ⑦ = =1 ⑧ - =-⑨ a-5= ×2-5=1-5=-4 ⑩ - a+1=- ×2+1=-1+1=0 ⑪ 1+a=1+ =1 ⑫ -a-3=- -3=-3 ⑬ 4a=4× =2 ⑭ -6a=-6× =-3 ⑮ 2a-5=2× -5=1-5=-4 � 8a+6=8× +6=4+6=10 � = = ÷5= × = <다른 풀이> = a= × =1 10 1 2 1 5 1 5 a 5 1 10 1 5 1 2 1 2 1 2 5 a 5 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 4 a 4 2 2 a 2 � = =5÷ =5×2=10 � 1- a=1- × =1- = � a- = × - = - = - =-1 6 3 6 2 6 1 2 1 3 1 2 1 2 2 3 1 2 2 3 3 4 1 4 1 2 1 2 1 2 1 2 5 1 2 5 a ① 5 ② -1 ③ -9 ④ 15 ⑤ 0 ⑥ -17 ⑦ -1 ⑧ - ⑨ 3 ⑩ 1 ⑪ ⑫ - ⑬ - ⑭ 3 ⑮ 0 � 4 � - � - � � -11 9 1 6 1 5 1 12 2 3 2 3 2 3 2 3 1 3 2 3 <풀이> ※ 음수를 대입할 때에는 ( )를 이용한다. ① 2-a=2-(-3)=2+3=5 ② 1 +a=1 +(-3)=1 -3=-1 ③ 3a=3×(-3)=-9 ④ -5a=-5×(-3)=15 ⑤ 2a+6=2×(-3)+6=-6+6=0 ⑥ -5+4a=-5+4×(-3)=-5-12=-17 ⑦ = =-1 ⑧ = =-⑨ a+4= ×(-3)+4=-1+4=3 ⑩ - a= - ×(-3)= + =1 ⑪a+1=- +1= ⑫ -1-a1-&- *1+ =-⑬ 2a=2×&- *=-⑭ -9a=-9×&- *=3 ⑮ 3a+1=3×&- *+1=-1+1=01 3 1 3 2 3 1 3 2 3 1 3 1 3 2 3 1 3 3 4 1 4 1 4 1 4 1 4 1 4 1 3 1 3 1 3 -3 9 a 9 3 -3 3 a 2 3 1 3 1 3 1 3

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## K-4

### 정답및풀이

� 4-2a=4-2×&- *=4+ =4 � = =&- *÷4=&- *× =-<다른 풀이> = a= ×&- *=-� = = =-� a+ = ×&- *+ =- + =- + = � -1+ a=-1+ ×&- *=-1- =-11 9 1 9 1 3 1 3 1 3 1 6 2 6 1 6 1 3 1 6 1 3 1 3 1 2 1 3 1 2 1 5 -1 5 5 3a 5 1 12 1 3 1 4 1 4 a 4 1 12 1 4 1 3 1 3 4 a 4 2 3 2 3 1 3 -1 3 3×&- *1 3 ① 4 ② -8 ③ 16 ④ -32 ⑤ 64 ⑥ 8 ⑦ -16 ⑧ 32 ⑨ -64 ⑩ 128 ⑪ 1 ⑫ ⑬ 2 ⑭ ⑮ � 2 � 1 � - � -1 � -5 4 5 8 1 4 3 16 1 8 1 4 <풀이> ①x2 =(-2)2 =4 ②x3=(-2)3=-8 ③x4=(-2)4=16 ④x5=(-2)5=-32 ⑤x6 =(-2)6 =64 ⑥ 2x2=2×(-2)2=2×4=8 ⑦ 2x3=2×(-2)3=2×(-8)=-16 ⑧ 2x4=2×(-2)4=2×16=32 ⑨ 2x5 =2×(-2)5 =2×(-32)=-64 ⑩ 2x6=2×(-2)6=2×64=128 ⑪ = =1 ⑫ = = ⑬ = = = =2 ⑭ = = = ⑮ = = = =3 16 6 32 6 2×16 6 2×24 6 2x4 1 8 2 16 2 24 2 x4 16 8 16 2×4 16 2×22 16 2x2 1 4 1 22 1 x2 2 2 2 x � - = - = =2 � + = + = + = =1 � - - =- - = - - - =-� - + =- + =- + =- + =- =-� = = =10=-5 -2 10 2-4 10 2-22 10 x-x2 1 4 3 12 2 12 5 12 1 6 5 3×4 1 3×2 5 3×22 1 3x 5 3x2 5 8 3 8 2 8 3 8 1 4 3 23 1 2×2 3 x3 1 2x 1 4 5 4 2 4 3 4 1 2 3 22 1 x 3 x2 4 2 1 2 5 2 1 2 5 x ① -6 ② 27 ③ 36 ④ -54 ⑤ 0 ⑥ 18 ⑦ -24 ⑧ 72 ⑨ 15 ⑩ -39 ⑪ ⑫ - ⑬ ⑭ - ⑮ � -1 � 1 � -1 � 1 � -1 3 1 3 1 9 1 9 1 9 1 9 <풀이> ① 2x=2×(-3)=-6 ② 3x2=3×(-3)2=3×9=27 ③ 4x2=4×(-3)2=4×9=36 ④ 2x3 =2×(-3)3 =2×(-27)=-54 ⑤x2 +3x=(-3)2 +3×(-3)=9-9=0 ⑥x2-3x=(-3)2-3×(-3)=9+9=18 ⑦x3-x=(-3)3-(-3)=-27+3=-24 ⑧x4 -x2 =(-3)4 -(-3)2 =81-9=72 ⑨ 4x+3x2 =4×(-3)+3×(-3)2 =-12+27=15 ⑩ 4x-3x2=4×(-3)-3×(-3)2=-12-27=-39 ⑪x2=& *2= ⑫ -x2=-& *2 =-⑬ (-x)2=&- *2= ⑭ -(-x)2 =-&- * 2 =-1 9 1 3 1 9 1 3 1 9 1 3 1 9 1 3

(9)

⑮ 3x2 =3×& * 2 =3× = � -3x2=-3×& *2 =-� (3x)2=&3× *2=12=1 � -(3x)2=-&3× *2=-12=-1 � (-3x)2 =&-3× * 2 =(-1)2 =1 � -(-3x)2=-&-3× *1 2=-(-1)2=-1 3 1 3 1 3 1 3 1 3 1 9 1 3 1 3 1 9 1 3 ⑩ b = ×& * = -=- - =-⑪ = = = =1 ⑫ = = = =-1 ⑬ &2b+ *= ×“2×&- *+ ‘ = ×&-1+ * = ×&- *=-⑭ & -5b*= ×“ -5×&- *‘ = ×& + * = ×3= =1 ⑮ - +(-b)2 =- +“-&- *‘ 2 =- +& * 2 =- + =0 � 3b3+ =3×&- *3+ =3×&- *+ =- + =- + =-7 40 8 40 15 40 1 5 3 8 1 5 1 8 1 5 1 2 1 5 1 4 1 4 1 2 1 4 1 2 1 4 1 4 1 2 3 2 1 2 5 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 6 2 3 1 4 1 3 1 4 1 3 1 2 1 4 1 3 1 4 1 2 -3 2 4-7 2 2 -8b-7 2 5 5 2+3 5 5 -4b+3 5 7 10 5 10 2 10 1 2 1 5 1 2 1 2 2 5 1 2 2 5 <풀이> ① = = = =1 ② = = = =-2 ③ = = = ④ = = = =-=-2 ⑤ - =- =- =-⑥ - b+ ×2+ 1+ =-⑦ - - b=- - ×2=- - =- =-2 ⑧ 7.5b-0.5=7.5×2-0.5=15-0.5=14.5 ⑨ 3b+3=3×&- *+3=- +3=-1 +3=11 2 1 2 3 2 1 2 6 3 5 3 1 3 5 6 1 3 5 6 1 3 2 3 1 3 1 3 1 2 1 3 1 2 1 2 5-4 2 5-2×2 2 5-2b 2 1 2 5 2 -10 4 -8-2 4 -4×2-2 4 -4b-2 4 2 3 -10+12 3 -5×2+12 3 -5b+12 3 -4 2 6-10 2 3×2-10 2 3b-10 2 3 4 7 4 4+3 4 2×2+3 4 2b+3 4 ① 1 ② -2 ③ ④ -2 ⑤ - ⑥ - ⑦ -2 ⑧ 14.5 ⑨ 1 ⑩ - ⑪ 1 ⑫ -1 ⑬ - ⑭ 1 ⑮ 0 � -7 40 1 2 1 6 1 2 7 10 1 2 2 3 1 2 1 2 2 3 3 4 -4×&- *+31 2 -8×&- *-71 2 ① -2 ② 17 ③ -5 ④ ⑤ 1 ⑥ 7 ⑦ -4 ⑧ -10 ⑨ ⑩ ⑪ ⑫ -⑬ 0 ⑭ -3 ⑮ 1 � -1 8 1 8 1 4 1 4 3 8 1 4 1 4 1 2 1 2 14 15 2 3

(10)

## K-4

### 정답및풀이

<풀이> ① 3b+4=3×(-2)+4=-6+4=-2 ② -5b+7=-5×(-2)+7=10+7=17 ③ b-5= ×(-2)-5=- -5=-5 ④ - b- =- ×(-2)-= - ×(-2)-= - = ⑤ = = = = =1 ⑥ - =-=- =- = =7 ⑦ (-3b-20)= ×{-3×(-2)-20} = ×(6-20)= ×(-14)=-4 ⑧ 4.3b-1.4=4.3×(-2)-1.4=-8.6-1.4=-10.0 ⑨b2=&- *2= ⑩ (-b)2=“-&- *‘2=& *2= ⑪ -3b3 =-3×&- * 3 =-3×&- *= ⑫b2 +b=&- * 2 +&- *= - = - =-⑬ -2b2-b=-2×&- *2-&- * =-2× + =- + =0 ⑭ -b2+6b=-&- *2+6×&- *=- -3=-3 ⑮ 3b3 -3b=3×&- * 3 -3×&- * =3×&- *+ =- + =- + = =1 � - b-(-b)2 =- ×&- *-“-&- *‘ 2 = -& *2= -= - -=-1 8 2 8 1 8 1 4 1 8 1 2 1 8 1 2 1 2 1 4 1 4 1 8 9 8 12 8 3 8 3 2 3 8 3 2 1 8 1 2 1 2 1 4 1 4 1 2 1 2 1 2 1 2 1 2 1 4 1 2 1 2 1 4 2 4 1 4 1 2 1 4 1 2 1 2 3 8 1 8 1 2 1 4 1 2 1 2 1 4 1 2 2 7 2 7 2 7 2 7 1 2 15 2 -15 2 -8-7 2 4×(-2)-7 2 4b-7 2 1 2 3 2 6 4 -4+10 4 2×(-2)+10 4 2b+10 4 14 15 10 15 24 15 2 3 8 5 2 3 4 5 2 3 4 5 2 3 2 3 1 3 1 3 ① -2 ② 1 ③ ④ -⑤ ⑥ - ⑦ -1 ⑧ -⑨ 20 ⑩ -1 ⑪ 2 ⑫ -3 ⑬ 50 ⑭ -50 ⑮ -9 � 9 10 1 2 1 2 2 3 1 6 1 4 1 12 1 6 1 4 1 8 9 20 3 8 1 3 <풀이> ① = = = =-2 ② = = = =1 ③ = = = = × = ④ = = = =&- *× =-⑤ = = = = × = ⑥ - =-=- =-=-& × *=-1 4 1 10 5 2 10 10 10 4+6y 10 1 8 1 6 3 4 6 6 6 2+5y 6 9 20 1 5 9 4 5 5 5 -3y-3 5 3 8 1 4 3 2 4 4 4 -2y+1 4 2 2 -2+4 2 2 8y+4 2 1 3 -7 3 -1-6 3 3 4y-6 3 4×&- *-61 4 8×&- *+41 4 -2×&- *+11 4 +1 1 2 1 1 2 2+5×&- *1 4 4+6×&- *1 4 2-5 4 -21 4 3 4 4-3 2 5 2 -3×&- *-31 4 -3 3 4

(11)

⑦ 2y- =2×&- *= *= -=- -=-1 ⑧ - -3y=- -3×&- * =- + =- + =-⑨ 4y+ =4×5+ =20+ =20 ⑩ - + =- + =- + =- =-1 ⑪ - + y=- + ×5 =- + =- + = = =2 ⑫ (-4-2y)= ×(-4-2×5) = ×(-4-10) = ×(-14) =- =-3 ⑬ (2y)2 -50=(2×5)2 -50 =102 -50 =100-50=50 ⑭ -(-2y)2+50=-(-2×5)2+50 =-(-10)2 +50 =-100+50=-50 ⑮ -10= -10 = -10 = -10=-9 � - + =- + =- + = + = + =9 10 4 10 5 10 2 5 1 2 2 5 -25 50 2 5 -52 50 2 5 -y2 50 1 2 1 2 25 50 (-5)2 50 (-y)2 50 1 2 7 2 1 4 1 4 1 4 1 4 2 3 8 3 16 6 21 6 5 6 7 2 5 6 7 10 5 6 7 10 5 6 1 6 7 6 3 6 10 6 1 2 5 3 1 2 y 3 1 4 1 4 1 4 1 4 1 12 9 12 10 12 3 4 5 6 1 4 5 6 5 6 1 6 7 6 4 6 3 6 2 3 1 2 2 3 1 4 2 3 ① 1 ② - ③ -3 ④ - ⑤ -⑥ ⑦ -1 ⑧ -23 4 1 18 1 5 2 15 1 12 1 4 2 5 <풀이> ① + = + = + = +1=1 ② + = + = + = - =-③ - = -= - -=0-3-=-3 ④ - = -= -=- + =-⑤ + = + = + = - =-⑥ - = -= - =- + = = ⑦ + = + = + =- -=- =-1 ⑧ - = -= - =- + =- =-23 4 11 4 11 4 22 4 -11 4 -11 2 2×(-3)-5 4 3×(-3)-2 2 2y-5 4 3y-2 2 1 18 19 18 16 18 3 18 -8 9 -1 6 4×(-3)+4 9 -3+2 6 4y+4 9 y+2 6 1 5 3 15 10 15 7 15 -2 3 -7 15 -3+1 3 2×(-3)-1 15 y+1 3 2y-1 15 2 15 12 15 10 15 -4 5 2 3 -3-1 5 -3+5 3 y-1 5 y+5 3 1 12 2 12 3 12 -1 6 -1 4 2×4-9 6 3×4-13 4 2y-9 6 3y-13 4 6 2 0 3 4+2 2 4-4 3 y+2 2 y-4 3 1 4 3 4 2 4 -3 4 1 2 2×4-11 4 4-3 2 2y-11 4 y-3 2 2 5 2 5 6 6 2 5 4+2 6 4-2 5 y+2 6 y-2 5

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## K-4

### 정답및풀이

① -3 ② 5 ③ -4 ④ ⑤ -25 ⑥ 25 ⑦ 50 ⑧ 100 ⑨ 35 ⑩ -70 ⑪ 50 ⑫ 45 5 24 1 2 3 4 <풀이> ① + = + = + =-3-=-3 ② - = = -=0+5=5 ③ + = + = + =- -=- =-=-4 ④ - = -= -=- + = ⑤ -b2=-(-5)2=-25 ⑥ (-b)2={-(-5)}2=52=25 ⑦ 2b2 =2×(-5)2 =2×25=50 ⑧ (2b)2 ={2×(-5)}2 =(-10)2 =100 ⑨b2-2b=(-5)2-2×(-5)=25+10=35 ⑩ -2b2+4b=-2×(-5)2+4×(-5) =-2×25-20 =-50-20=-70 ⑪b(b-5)=-5×(-5-5)=-5×(-10)=50 ⑫ (-2b)2+10b-5={-2×(-5)}2+10×(-5)-5 =102-50-5 =100-50-5 =50-5=45 5 24 44 24 39 24 -11 6 -13 8 4×(-4)+5 6 5×(-4)+7 8 4a+5 6 5a+7 8 1 2 9 2 27 6 7 6 20 6 -7 6 -10 3 -4-3 6 2×(-4)-2 3 a-3 6 2a-2 3 -15 3 0 7 3×(-4)-3 3 -4+4 7 3a-3 3 a+4 7 3 4 3 4 -3 4 -6 2 -4+1 4 -4-2 2 a+1 4 a-2 2 ① 3 ② - ③ 2 ④ 1 ⑤ -10 ⑥ - ⑦ ⑧ 0 ⑨ -9 ⑩ -9 ⑪ ⑫ ⑬ 4 ⑭ 4 ⑮ - � -1 10 1 10 3 4 3 4 2 3 2 3 1 27 1 27 1 2 11 12 2 3 <풀이> ① 4x+5=4×&- *+5=- +5=-1 +5=3 ② x- = ×&- *-=- - *-=- - =-③ = = = =2 ④ (-6x+4)= ×“-6×&- *+4‘ = ×(2+4) = ×6= =1 ⑤ 2(-3x-6)=2×“-3×&- *-6‘ =2×(1-6) =2×(-5)=-10 ⑥x3 =&- * 3 =-⑦ (-x)3 =“-&- *‘ 3 =& * 3 = ⑧ 1-(-3x)3=1-“-3×&- *‘3=1-13=1-1=0 ⑨ -5y= -5×2= -10=-9 ⑩ -5y+ =-5×2+ =-10+ =-9 ⑪ = = ⑫ - =- =- = ⑬ 10-(y3-y)=10-(23-2)=10-(8-2)=10-6=4 ⑭ 10-y3+y=10-23+2=10-8+2=2+2=4 3 4 -3 4 2-5 4 y-5 4 3 4 -2+5 4 -y+5 4 2 3 1 3 1 3 1 3 2 3 1 3 1 3 1 3 1 3 1 27 1 3 1 3 1 27 1 3 1 3 1 2 3 2 1 4 1 4 1 3 1 4 1 4 4 2 -3+7 2 2 9x+7 2 11 12 8 12 3 12 2 3 1 4 2 3 1 3 3 4 2 3 3 4 2 3 1 3 4 3 1 3 9×&- *+71 3

(13)

⑮ y2 - = ×22 - = ×4-= - ×4-= - =-� (y2 -5)= ×(22 -5) = ×(4-5) = ×(-1)=-1 10 1 10 1 10 1 10 1 10 1 10 5 10 4 10 1 2 2 5 1 2 1 10 1 2 1 10 1 2 1 10 ① 5 ② -1 ③ -1 ④ -8 ⑤ 3 ⑥ -2 ⑦ 0 ⑧ -2 ⑨ 16 ⑩ -2 ⑪ 6 ⑫ 0 ⑬ 6 ⑭ 18 ⑮ 12 � 13 � 5 � -10 1 2 <풀이> ①a+b=2+3=5 ②a-b=2-3=-1 ③ -2a+b=-2×2+3=-4+3=-1 ④ -a-2b=-2-2×3=-2-6=-8 ⑤a+ b=2+ ×3=2+1=3 ⑥ a-b= ×2-3=1-3=-2 ⑦ - a+ b=- ×2+ ×3=-1+1=0 ⑧ - a- b=- ×2- ×3=-1-1=-2 ⑨ 4a+2b=4×3+2×2=12+4=16 ⑩ 2a-4b=2×3-4×2=6-8=-2 ⑪ = = = =6 ⑫ = = = =0 ⑬ab=3×2=6 ⑭a2b=32×2=9×2=18 ⑮ab2=3×22=3×4=12 �a2 +b2 =32 +22 =9+4=13 �a2-b2=32-22=9-4=5 � -2a2+2b2=-2×32+2×22 =-2×9+2×4 =-18+8=-10 0 5 6-6 5 2×3-3×2 5 2a-3b 5 1 2 13 2 9+4 2 3×3+2×2 2 3a+2b 2 1 3 1 2 1 3 1 2 1 3 1 2 1 3 1 2 1 2 1 2 1 3 1 3 ① -5 ② 16 ③ -3 ④ 2 ⑤ 1 ⑥ ⑦ ⑧ -1 ⑨ 3 ⑩ 16 ⑪ -1 ⑫ -3 ⑬ -6 ⑭ 12 ⑮ -18 � 13 � -5 � 2 2 3 2 3 6 7 11 15 3 4 1 2 1 2 <풀이> ① 2x+3y=2×2+3×(-3)=4-9=-5 ② 5x-2y=5×2-2×(-3)=10+6=16 ③ -x+ y=-2+ ×(-3) =-2- =-2-1 =-3 ④ - -y=- -(-3)=- +3=2 ⑤ - y= - ×(-3)=1+ =1 ⑥ x+ = ×2+ = - = - = ⑦ = = = ⑧ = = = =-=-1 ⑨ 3x+3y=3×(-2)+3×3=-6+9=3 ⑩ -2x+4y=-2×(-2)+4×3=4+12=16 ⑪ = = = =-1 ⑫ = = = =-3 ⑬xy=(-2)×3=-6 ⑭x2y =(-2)2 ×3=4×3=12 ⑮xy2 =(-2)×32 =(-2)×9=-18 �x2+y2=(-2)2+32=4+9=13 �x2-y2=(-2)2-32=4-9=-5 � 5x2 -6y=5×(-2)2 -6×3 =5×4-18=20-18 =2 2 3 -11 3 -8-3 3 4×(-2)-3 3 4x-y 3 -4 4 2-6 4 -(-2)-2×3 4 -x-2y 4 2 3 5 3 -15 9 -12-3 9 -6×2+(-3) 9 -6x+y 9 6 7 -6+12 7 -3×2-4×(-3) 7 -3x-4y 7 11 15 9 15 20 15 3 5 4 3 -3 5 2 3 y 5 2 3 3 4 3 4 1 4 2 2 1 4 x 2 1 2 1 2 2 4 x 4 1 2 1 2 3 2 1 2 1 2

(14)

## K-4

### 정답및풀이

① -2 ② -13 ③ -17 ④ 24 ⑤ 29 ⑥ 47 ⑦ 7 ⑧ 91 ⑨ ⑩ -3 ⑪ - ⑫ 2 ⑬ - ⑭ ⑮ -1 �8 9 1 8 1 36 5 36 1 6 1 6 2 3 <풀이> ① 2a-b=2×(-3)-(-4)=-6+4=-2 ② -a+4b=-(-3)+4×(-4)=3-16=-13 ③ 3a+2b=3×(-3)+2×(-4)=-9-8=-17 ④ -4a-3b=-4×(-3)-3×(-4)=12+12=24 ⑤a+2b2=-3+2×(-4)2 =-3+2×16=-3+32=29 ⑥ 3a2-5b=3×(-3)2-5×(-4) =3×9+20=27+20=47 ⑦ -a2+b2=-(-3)2+(-4)2=-9+16=7 ⑧ -a3 -b3 =-(-3)3 -(-4)3 =-(-27)-(-64)=27+64=91 ⑨ 2x-y=2× - =1- = ⑩ -4x-3y=-4× -3× =-2-1=-3 ⑪ -x+y + + =-⑫ 3x+2y=3× +2× = + = + = =2 ⑬ -x2+y2=-& *2+& *2 =- + =- + =-⑭x2-2y2=& *2-2×& *2 = 2× = -= - = ⑮ -x3-9y2=-& *3-9×& *2 =- -9× =- -1=-1 � 4x2 -3y3 =4×& * 2 -3×& * 3 =4× -3× =1- =8 9 1 9 1 27 1 4 1 3 1 2 1 8 1 8 1 9 1 8 1 3 1 2 1 36 8 36 9 36 2 9 1 4 1 9 1 4 1 3 1 2 5 36 4 36 9 36 1 9 1 4 1 3 1 2 1 6 13 6 4 6 9 6 2 3 3 2 1 3 1 2 1 6 2 6 3 6 1 3 1 2 1 3 1 2 2 3 1 3 1 3 1 2 ① 9 ② 1 ③ 3 ④ -5 ⑤ 5 ⑥ -3 ⑦ -1 ⑧ -9 ⑨ -3 ⑩ 9 ⑪ 17 ⑫ -4 ⑬ 4 ⑭ 3 ⑮ 15 � 2 <풀이> ①a+b+c=2+3+4=9 ②a+b-c=2+3-4=1 ③a-b+c=2-3+4=3 ④a-b-c=2-3-4=-5 ⑤ -a+b+c=-2+3+4=5 ⑥ -a+b-c=-2+3-4=-3 ⑦ -a-b+c=-2-3+4=-1 ⑧ -a-b-c=-2-3-4=-9 ⑨a+b+c=(-2)+3+(-4)=-3 ⑩ -a+b-c=-(-2)+3-(-4)=2+3+4=9 ⑪ 2a-b-6c=2×(-2)-3-6×(-4) =-4-3+24=17 ⑫ -5a-2b+2c=-5×(-2)-2×3+2×(-4) =10-6-8=-4 ⑬ -a+6b+4c=-(-2)+6×3+4×(-4) =2+18-16=4 ⑭ -4a-3b-c=-4×(-2)-3×3-(-4) =8-9+4=3 ⑮ 6a+(5b-3c)=6×(-2)+{5×3-3×(-4)} =-12+(15+12)=-12+27=15 � 3a-(4b+5c)=3×(-2)-{4×3+5×(-4)} =-6-(12-20) =-6-(-8)=-6+8=2 ① 29 ② 11 ③ -20 ④ -17 ⑤ ⑥ -0.1 ⑦ - ⑧ 1 ⑨ - ⑩ -9 ⑪ -1 ⑫ 3 19 36 1 9 3 4 7 30 <풀이> ①a2 +b2 +c2 =42 +(-2)2 +(-3)2 =16+4+9=29 ②a2+b2-c2=42+(-2)2-(-3)2 =16+4-9=11 ③b2+2ac=(-2)2+2×4×(-3)=4-24=-20 ④ -c2 -2b-3a=-(-3)2 -2×(-2)-3×4 =-9+4-12=-17

(15)

⑤ - + = - + = + - = ⑥ -1.5a+0.5b-2.3c =-1.5×4+0.5×(-2)-2.3×(-3) =-6-1+6.9 =-0.1 ⑦ 3a+b2=3×&- *+&- *21+ =-⑧a2 +4b2 =&- * 2 +4×&- * 2 = +4× = +1=1 ⑨ 2a2-3b2=2×&- *2-3×&- *2 =2× -3× = - = - =-⑩a+(b-c)=-3+{(-4)-2} =-3+(-6)=-3-6=-9 ⑪a-(b+c)=-3-{(-4)+2} =-3-(-2)=-3+2=-1 ⑫a-(b-c)=-3-{(-4)-2} =-3-(-6)=-3+6=3 19 36 27 36 8 36 3 4 2 9 1 4 1 9 1 2 1 3 1 9 1 9 1 4 1 9 1 2 1 3 3 4 1 4 1 2 1 3 7 30 45 30 12 30 40 30 -3 2 -2 5 4 3 c 2 b 5 a 3 ⑤ = =- =-8 ⑥ = =- =-⑦a2×b3=(-2)2×23=4×8=32 ⑧a3×b2=(-2)3×22=(-8)×4=-32 ⑨a2+b2=(-2)2+(-3)2=4+9=13 ⑩a2 -b2 =(-2)2 -(-3)2 =4-9=-5 ⑪ (a+b)(a-b)={(-2)+(-3)}×{(-2)-(-3)} =(-5)×1=-5 ⑫a2+2ab+b2=(-2)2+2×(-2)×(-3)+(-3)2 =4+12+9=25 ⑬a2-2ab+b2=(-2)2-2×(-2)×(-3)+(-3)2 =4-12+9=1 ⑭ (a+b)2={(-2)+(-3)}2=(-5)2=25 ⑮ (a-b)2 ={(-2)-(-3)}2 =12 =1 � (a+b)3={(-2)+(-3)}3=(-5)3=-125 1 8 2×2×2 2×2×2×2×2×2 (-2)3 26 a3 b6 2×2×2×2×2 2×2 (-2)5 22 a5 b2 ① 2 ② - ③ -4 ④ ⑤ -8 ⑥ - ⑦ 32 ⑧ -32 ⑨ 13 ⑩ -5 ⑪ -5 ⑫ 25 ⑬ 1 ⑭ 25 ⑮ 1 � -125 1 8 1 4 1 2 <풀이> ① = = =2 ② = =- =-③ = =- =-4 ④ = = =1 4 2×2 2×2×2×2 (-2)2 24 a2 b4 2×2×2 2 (-2)3 2 a3 b 1 2 2 2×2 -2 22 a b2 2×2 2 (-2)2 2 a2 b ① ② -1 ③ -3 ④ -26 ⑤ -1 ⑥ 1 ⑦ -14.9 ⑧ 7 ⑨ 31 ⑩ -21 ⑪ -14 ⑫ 10 2 9 2 3 1 4 <풀이> ① 1- =1- =1- = ② = = =- =- =-1 ③ -5= -5= -5=1 -5=-3 ④ 10+xy2=10+(-4)×(-3)2 =10+(-4)×9=10-36=-26 ⑤ (x-y)3={(-4)-(-3)}3=(-1)3=-1 ⑥ (y-x)3={(-3)-(-4)}3=13=1 ⑦ -0.7x+2.5y+3.5z =-0.7×(-3)+2.5×(-4)+3.5×(-2) =2.1-10-7=-14.9 ⑧ = = =14=7 2 -6+12+8 2 2×(-3)-3×(-4)-4×(-2) 2 2x-3y-4z 2 2 9 7 9 16 9 (-4)2 (-3)2 x2 y2 2 3 5 3 20 12 16+4 -12 (-4)2 +4 4×(-3) x2 +4 4y 1 4 3 4 -3 -4 y x

(16)

## K-4

### 정답및풀이

⑨x2+xz+y2=(-3)2+(-3)×(-2)+(-4)2 =9+6+16=31 ⑩ -y2 -yz-x=-(-4)2 -(-4)×(-2)-(-3) =-16-8+3=-21 ⑪ -z2+xz-y2=-(-2)2+(-3)×(-2)-(-4)2 =-4+6-16=-14 ⑫xy-yz+xz =(-3)×(-4)-(-4)×(-2)+(-3)×(-2) =12-8+6=10 ① 2 ② -32 ③ ④ -⑤ 16 ⑥ 0 ⑦ ⑧ -1 ⑨ - ⑩ -1 ⑪ 9 ⑫ -9 3 7 12 1 12 7 12 2 3 5 6 <풀이> ① -4-xyz=-4-1×(-2)×3=-4+6=2 ②y2(x2-z2)=(-2)2×(12-32) =4×(1-9)=4×(-8)=-32 ③ + + = + + =1- + = ④ = = =-⑤ (x+y-z)2={1+(-2)-3}2=(-4)2=16 ⑥x2 -(y+z)2 =12 -{(-2)+3}2 =1-12 =1-1=0 ⑦ + - = + -=- + + = ⑧ - + = - + =- - - =- =-1 ⑨ - - + =- - + = - - =-⑩ = = =- =-⑪ (x+y+z)2={(-4)+3+(-2)}2=(-3)2=9 ⑫x2 -(y-z)2 =(-4)2 -{3-(-2)}2 =16-52=16-25=-9 1 3 4 12 (-2)2 -12 {(-4)-(-2)}2 2×3×(-2) (x-z)2 2yz 7 12 6 12 4 12 3 12 1 -2 1 3 1 -4 1 z 1 y 1 x 1 12 13 12 6 12 4 12 3 12 1 -2 1 3 1 -4 1 z 1 y 1 x 7 12 6 12 4 12 3 12 1 -2 1 3 1 -4 1 z 1 y 1 x 2 3 4 -6 1+3 (-2)×3 x+z yz 5 6 2 6 3 6 1 3 1 -2 1 1 1 z 1 y 1 x ① 1 ② 3 ③ - ④ 4 ⑤ 1 ⑥ -6 ⑦ -2 ⑧ -⑨ 7 ⑩ -0.4 ⑪ 0.4 12 1 12 1 12 2 3 1 3 2 3 <풀이> ① 1- =1- =1+ =1 ② 1- =1- =1+ =1+2 =3 ③ 1- =1- =1- =-④ 1- =1- =1+3=4 ⑤ 1- =1- =1-&- *× =1+ =1 ⑥a-(b+c)=3-(4+5)=3-9=-6 ⑦a-(b+c)=-3-{4+(-5)}=-3+1=-2 ⑧a-(b+c)= -& + * = -& + * = - =-⑨a-(b+c)= -&- + * = -&- + *= + = ⑩a-(b+c)=0.1-(0.2+0.3)=0.1-0.5=-0.4 ⑪a-(b+c)=-0.1-{(-0.2)+(-0.3)} =-0.1+0.5 =0.4 7 12 1 12 6 12 3 12 4 12 6 12 1 4 1 3 1 2 1 12 7 12 6 12 3 12 4 12 6 12 1 4 1 3 1 2 1 12 1 12 1 3 1 4 3 a b 0.9 -0.3 a b 2 3 5 3 -15 -9 a b 1 3 1 3 7 3 -14 6 a b 2 3 2 3 2 -3 a b -1 4 ① ② ③ - ④ ⑤ -1 ⑥ ⑦ ⑧ -⑨ ⑩ 1 18 1 4 7 24 1 2 1 20 1 4 9 14 9 14 5 6 1 6

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① 7a ② 14b ③ 3x ④ -3y ⑤ -6b ⑥ 7a ⑦ -8y ⑧ 13x ⑨ a ⑩ - x ⑪ - y ⑫ b ⑬ b ⑭ -a ⑮ - b �1y 5 2 3 6 7 5 9 2 3 5 8 3 5 <풀이> ※ 여기에서는 암산으로 계산을 하여 답을 써야 한다. 다음 풀이는 암산이 안 되는 학생들을 위 하여 써 놓은 것이므로, 계산 과정을 참조하여 답만 쓰도록 한다. ① 4a+3a=(4+3)a=7a ② 6b+8b=(6+8)b=14b ③ 7x-4x=(7-4)x=3x ④ 8y-11y=(8-11)y=-3y ⑤ -9b+3b=(-9+3)b=-6b ⑥ -7a+14a=(-7+14)a=7a ⑦ -6y-2y=(-6-2)y=-8y ⑧ 5x+8x=(5+8)x=13x ⑨ a+ a=& + *a= a ⑩ -x+ x=&-1+ *x=- x ⑪ - y- y=&- - *y=- y ⑫ b- b=& - *b= b ⑬ b+ b=& + *b= b ⑭ - a- a=&- - *a=- a=-a ⑮ - b+ b=&- + *b=- b=- b � y- y=& - *y= y=1y 5 2 10 7 10 9 10 7 10 9 10 2 3 4 6 1 6 5 6 1 6 5 6 4 4 1 4 3 4 1 4 3 4 6 7 1 7 5 7 1 7 5 7 5 9 2 9 7 9 2 9 7 9 2 3 1 3 1 3 1 3 1 3 5 8 3 8 3 8 3 5 2 5 1 5 2 5 1 5 ① 11a ② -6x ③ 8b ④ -13y ⑤ 15a ⑥ 6x ⑦ -4a ⑧ 0 ⑨ -4b ⑩ 3y ⑪ - x ⑫ b ⑬ - y⑭ x ⑮ b � 0 � -13a 12 1 10 17 12 19 12 3 8 1 6 <풀이> ※ ①~⑩까지는 가능하면 암산을 하여 답만 쓰 도록 한다. ① 6a-(-5a)=6a+5a=(6+5)a=11a ② 3x+(-9x)=3x-9x=(3-9)x=-6x ③ -7b-(-15b)=-7b+15b=(-7+15)b=8b ④ -5y+(-8y)=-5y-8y=(-5-8)y=-13y <풀이> ① - = - = - = - = ② - = - = + = + = ③ - = -=- - -=- - =-④ - = -= + -= + = ⑤ - = - =- -1=-1 ⑥ - = -= - -= - = ⑦ - = -= + -= + -= -= ⑧ - = -=- - -=- - =-⑨ - = -=- + -=- + = ⑩ - = -=- + -=- + =1 18 3 18 2 18 1 6 1 9 1 -6 1 (-4)+(-5) 1 z 1 x+y 1 4 2 4 1 4 1 2 1 4 1 -2 1 3+(-7) 1 z 1 x+y 7 24 4 24 3 24 1 6 1 8 1 6 1 (-5)+(-3) 1 z 1 x+y 1 2 3 6 2 6 1 6 1 3 1 6 1 -3 1 4+2 1 z 1 x+y 1 20 4 20 5 20 1 5 1 4 1 5 1 1+3 1 z 1 x+y 1 4 1 4 1 3+(-2) 1 -4 1 y+z 1 x 9 14 2 14 7 14 1 7 1 2 1 -4-3 1 2 1 y+z 1 x 9 14 2 14 7 14 1 7 1 2 1 3+4 1 -2 1 y+z 1 x 5 6 3 6 2 6 1 2 1 3 1 -4+2 1 3 1 y+z 1 x 1 6 1 6 2 6 1 6 1 3 1 2+4 1 3 1 y+z 1 x

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## K-4

### 정답및풀이

⑤ 6a-(-5a)+4a=6a+5a+4a =(6+5+4)a=15a ⑥ -2x-(-3x)-(-5x)=-2x+3x+5x =(-2+3+5)x=6x ⑦a-7a+2a=(1-7+2)a=-4a ⑧ -4x+5x-x=(-4+5-1)x=0 ⑨ 3b-4b+2b-5b=(3-4+2-5)b=-4b ⑩ -2y+4y+7y-6y=(-2+4+7-6)y=3y ⑪ - x= x- x=& - *x=- x ⑫ - b+ b=- b+ b=&- + *b= b ⑬ - y- y=- y- y =&- - *y=- y ⑭ + + x= x+ x+ x =& + + *x= x ⑮b- b- b= b- b- b =& - - *b= b � - y+ y+ y=- y+ y+ y =&- + + *y =0 � - a- a+ a=- a- a+ a =&- - + *a =-13a 12 6 12 9 12 10 12 6 12 9 12 10 12 1 2 3 4 5 6 2 6 1 6 3 6 2 6 1 6 3 6 1 3 1 6 1 2 1 10 4 10 5 10 10 10 4 10 5 10 10 10 2 5 1 2 17 12 3 12 8 12 6 12 3 12 8 12 6 12 1 4 2x 3 x 2 19 12 10 12 9 12 10 12 9 12 5 6 3 4 3 8 6 8 3 8 6 8 3 8 3 4 3 8 1 6 3 6 2 6 3 6 2 6 1 2 x 3 ① 4x+5 ② 4x-1 ③ -4x+1 ④ -4x-1 ⑤ -4x-5 ⑥ 4x+5 ⑦ 4x+1 ⑧ -4x+1 ⑨ 4x-5 ⑩ -4x-5 ⑪ 5x+9 ⑫ -x-9 ⑬ -5x+9 ⑭x+1 ⑮ -5x-9 � 5x-1 � -x+1 �x-1 �x+1 � -5x+1 <풀이> ① 4x+3+2=4x+5 ② 4x-3+2=4x-1 ③ -4x+3-2=-4x+1 ④ -4x-3+2=-4x-1 ⑤ -4x-3-2=-4x-5 ※ 다음 풀이는 암산이 안 되는 학생들을 위하 여 써 놓은 것이므로, 계산 과정을 참조하여 답 만 쓰도록 한다. ⑥ 3+4x+2=4x+3+2=4x+5 ⑦ 3+4x-2=4x+3-2=4x+1 ⑧ 3-4x-2=-4x+3-2=-4x+1 ⑨ -3+4x-2=4x-3-2=4x-5 ⑩ -3-4x-2＝-4x-3-2=-4x-5 ⑪ 2x+3x+4+5=5x+9 ⑫ 2x-3x-4-5=-x-9 ⑬ -2x-3x+4+5=-5x+9 ⑭ -2x+3x-4+5=x+1 ⑮ -2x-3x-4-5=-5x-9 ※ 다음 풀이는 암산이 안 되는 학생들을 위하 여 써 놓은 것이므로, 계산 과정을 참조하여 답 만 쓰도록 한다. � 2x+4+3x-5=2x+3x+4-5=5x-1 � 2x-4-3x+5=2x-3x-4+5=-x+1 � -2x+4+3x-5=-2x+3x+4-5=x-1 � -2x-4+3x+5=-2x+3x-4+5=x+1 � -2x-4-3x+5=-2x-3x-4+5=-5x+1 ① 6y ② -5y ③ 10y ④ -9y+10 ⑤ 2y-3 ⑥ 6y ⑦ 2y-5 ⑧ -6y+7 ⑨ 5y -⑩ - y+8 ⑪ -4y ⑫ -5y+2 ⑬ -10y-7 ⑭ 5y+10 ⑮ 9y � 2 � -13y-8 � -12y-7 � - y+9 �1y+2 3 11 12 1 18 1 6 <풀이> ※ 가능하면 암산을 하여 답만 쓰도록 한다. ① -8y+14y=6y ② 6y+(-11y)=6y-11y=-5y ③ 3y+2y+5y=10y ④ 4-9y+6=-9y+4+6=-9y+10

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⑤ -5y-(-7y)-3=-5y+7y-3=2y-3 ⑥ 4y+5y-6y+3y=6y ⑦ -7+8+2y-6=2y-7+8-6=2y-5 ⑧ -2y-(-9)+(-2)-4y=-2y-4y+9-2 =-6y+7 ⑨ - +5y+ =5y- + =5y -⑩ 4- y+ y+4=- y+ y+4+4 =- y+8 ⑪ 2y+4y-10y=-4y ⑫ -4-5y+6=-5y-4+6=-5y+2 ⑬ -7y+(-3y)-7=-7y-3y-7=-10y-7 ⑭ 5y+4+1+5=5y+10 ⑮ -y+5y+2y+3y=9y � 6y-2-6y+4=6y-6y-2+4=2 �y-8-9y-5y=y-9y-5y-8=-13y-8 � -2y+(-3)-4+(-10y)=-2y-10y-3-4 =-12y-7 � 9- y- y=- y- y+9=- y+9 � - y+7-5+ y＝- y+ y+7-5 = y+2=1y+2 3 2 6 5 6 3 6 5 6 1 2 11 12 8 12 3 12 2 3 1 4 1 18 2 18 3 18 1 9 1 6 1 6 2 6 3 6 1 3 1 2 ⑧ -6a-2b+13a=-6a+13a-2b=7a-2b ⑨ -8a-5b-7a=-8a-7a-5b=-15a-5b ⑩ -10a+4b+8a=-10a+8a+4b=-2a+4b ⑪ 2a-5b-3a+4b=2a-3a-5b+4b=-a-b ⑫ 2a+5b+3a+4b=2a+3a+5b+4b=5a+9b ⑬ 2a+5b-3a+4b=2a-3a+5b+4b=-a+9b ⑭ 2a-5b+3a-4b=2a+3a-5b-4b=5a-9b ⑮ 2a-5b-3a-4b=2a-3a-5b-4b=-a-9b � -2a+5b-3a+4b=-2a-3a+5b+4b =-5a+9b � -2a+5b+3a+4b=-2a+3a+5b+4b=a+9b � -2a+5b-3a-4b=-2a-3a+5b-4b =-5a+b � -2a-5b+3a+4b=-2a+3a-5b+4b=a-b � -2a-5b-3a-4b=-2a-3a-5b-4b =-5a-9b <풀이> ※ 가능하면 암산을 하여 답만 쓰도록 한다. ①a+3b+5a=a+5a+3b=6a+3b ② 4a+4b-7a=4a-7a+4b=-3a+4b ③ 3a-5b+4a=3a+4a-5b=7a-5b ④ 3a-2b-8a=3a-8a-2b=-5a-2b ⑤ 9a-b+3a=9a+3a-b=12a-b ⑥ -2a+6b+6a=-2a+6a+6b=4a+6b ⑦ -7a+3b-4a=-7a-4a+3b=-11a+3b ① 6a+3b ② -3a+4b ③ 7a-5b ④ -5a-2b ⑤ 12a-b ⑥ 4a+6b ⑦ -11a+3b ⑧ 7a-2b ⑨ -15a-5b ⑩ -2a+4b ⑪ -a-b ⑫ 5a+9b ⑬ -a+9b ⑭ 5a-9b ⑮ -a-9b � -5a+9b �a+9b � -5a+b �a-b � -5a-9b ① 8x+5y ② 8x+y ③ -2x-y ④ 8x-5y ⑤ -2x-5y ⑥ 2x+5y ⑦ 2x-y ⑧ -8x+5y ⑨ 2x-5y ⑩ -8x+y ⑪ 6a+2b ⑫ -13x+5y ⑬ -3a-4x ⑭ 2b-3y ⑮ 10a+4b � -x+5y � 7a-9y � -5b+12x � - a+ b � x-3y 4 2 5 1 2 1 3 <풀이> ※ 가능하면 암산을 하여 답만 쓰도록 한다. ① 3x+2y+5x+3y=3x+5x+2y+3y=8x+5y ② 3x-2y+5x+3y=3x+5x-2y+3y=8x+y ③ 3x+2y-5x-3y=3x-5x+2y-3y=-2x-y ④ 3x-2y+5x-3y=3x+5x-2y-3y=8x-5y ⑤ 3x-2y-5x-3y=3x-5x-2y-3y=-2x-5y ⑥ -3x+2y+5x+3y=-3x+5x+2y+3y =2x+5y ⑦ -3x+2y+5x-3y=-3x+5x+2y-3y =2x-y ⑧ -3x+2y-5x+3y=-3x-5x+2y+3y =-8x+5y ⑨ -3x-2y+5x-3y=-3x+5x-2y-3y =2x-5y ⑩ -3x-2y-5x+3y=-3x-5x-2y+3y =-8x+y ⑪ 8a+2b-2a=8a-2a+2b=6a+2b ⑫ -4x+5y-9x=-4x-9x+5y=-13x+5y

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## K-4

### 정답및풀이

⑬a+(-4x)-4a=a-4x-4a =a-4a-4x=-3a-4x ⑭ -5b-3y-(-7b)=-5b-3y+7b =-5b+7b-3y=2b-3y ⑮ 5a-3b+7b+5a=5a+5a-3b+7b=10a+4b � -5x+6y+4x-y=-5x+4x+6y-y=-x+5y � 9a-2a-5y+(-4y)=9a-2a-5y-4y =7a-9y � -2b-(-8x)+(-3b)+4x=-2b+8x-3b+4x =-2b-3b+8x+4x =-5b+12x � -a+ b+ a=-a+ a+ b=- a+ b �x-y- x+ y=x- x-y+ y= x-3y 4 2 5 1 4 3 5 1 4 3 5 1 2 1 3 1 2 2 3 2 3 1 2 ① 7a ② -14b ③ - x ④ y ⑤ a ⑥ - x ⑦ -7a ⑧ 16a-5b ⑨ x ⑩ - b- x ⑪ x-y ⑫ 5x ⑬ 15a+ x ⑭a- y ⑮ - b+ x � - x-7y 12 3 8 4 7 1 3 5 12 1 5 2 9 1 2 3 4 1 30 1 6 4 7 1 6 2 5 <풀이> ※ 가능하면 암산을 하여 답만 쓰도록 한다. ① 2a+5a=7a ② -8b+(-6b)=-8b-6b=-14b ③ x-x=- x ④ - y-(-y)=- y+y= y ⑤ a- a= a ⑥ - x+ =- x+ x=- x ⑦ 8a+5a-20a=-7a ⑧ 9a+(-5b)+7a=9a+7a-5b=16a-5b ⑨ - + + =- x+ x+ x=1x 30 6 30 10 30 15 30 x 5 x 3 x 2 1 6 4 6 5 6 2x 3 5 6 4 7 2 7 6 7 1 6 5 6 5 6 2 5 3 5 ⑩ -b-&- b*- x=-b+ b- x =- b- x ⑪ x-y- x= x- x-y= x-y ⑫ 4x-7x+5x+3x=5x ⑬ 3a+ x+4a+8a=3a+4a+8a+ x =15a+ x ⑭a+ y- y- y=a+ y- y- y =a- y ⑮ -b+ b- x+x=- b+ x � - x- y+ x- y =- x+ x- y- y=- x-7y 12 3 8 3 12 4 12 4 8 7 8 1 4 1 2 1 3 7 8 4 7 1 3 3 7 2 3 5 12 6 12 2 12 3 12 1 2 1 6 1 4 1 5 1 5 1 5 2 9 3 9 5 9 1 3 5 9 1 2 3 4 1 2 1 4 1 2 1 4 ① a ② - x ③ b ④ -y ⑤ a ⑥ - x ⑦ b ⑧ 5a+ x ⑨ - b+ y ⑩ - a-b ⑪ - x- y ⑫ y+8 ⑬ a+ b ⑭ - x+ y ⑮ - a- x � - b+1y 18 9 4 4 5 13 10 9 4 7 6 13 6 17 5 13 3 5 6 5 4 3 2 2 3 12 5 4 3 7 2 2 15 5 14 5 2 7 2 8 3 <풀이> ※ 답을 대분수로 고치지 않고 가분수로 쓴다. ① 2a+ a= a ② x-4x=- x ③ -3b+ b= b ④ - y-3y=-y 4 1 4 5 2 11 2 7 2 1 2 8 3 2 3

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⑤ a- a= a- a= a ⑥ - x+ x=- x+ x=- x ⑦b+2b+ = b ⑧ 5a-2x+ x=5a+ x ⑨ - b-2b+ y=- b+ y ⑩ a-b- a= a- a-b=- a-b=- a-b ⑪ - x- y- x=- x- x- y =- x- y ⑫ 4y+5+3+ y=4y+ y+5+3= y+8 ⑬ 5a+ b- a+2b=5a- a+ b+2b = a+ b ⑭ x- x- y+3y= x- x- y+3y =- x+ y ⑮ - a+ x- a-x=- a- a+ x-x =- a- x � - b- y+ y- b =- b- b- y+ y=- b+1y 18 9 4 3 18 2 18 6 4 3 4 3 2 1 6 1 9 3 4 4 5 13 10 1 5 8 10 5 10 4 5 1 5 1 2 9 4 7 6 3 4 15 6 8 6 3 4 5 2 4 3 13 6 17 5 1 6 8 5 8 5 1 6 13 3 1 3 1 3 5 6 5 4 5 6 3 4 2 4 3 4 5 6 1 2 3 2 6 4 7 4 1 4 7 4 1 4 2 3 12 5 2 3 2 5 4 3 10 3 7 2 b 2 2 15 18 15 20 15 6 5 4 3 5 14 2 14 7 14 1 7 1 2 ①a+4b ② -9a+8b ③ 3a-2b ④ -4x-5y ⑤ -18x+7y ⑥ 12x-17y ⑦ 6a+3b-5 ⑧ -9a+9b+8 ⑨ 3x+15y-8 ⑩ -12x-11 ⑪a-2b+3c ⑫ -3a-10b+6c ⑬ -16x+8y-4z ⑭ 4x+5y-11z ⑮ -7x2+5 � 8x2+14x-3 � 2x2+6x-3 � -5x2-12x-4 <풀이> ※ 가능하면 암산을 하여 답만 쓰도록 한다. ① 7a-6a+b+3b=a+4b ② -2a+5b-7a+3b=-2a-7a+5b+3b =-9a+8b ③ -8a-4b+2b+11a =-8a+11a-4b+2b =3a-2b ④ 5x-13y-9x+8y=5x-9x-13y+8y =-4x-5y ⑤ -9x+15y-8y-9x=-9x-9x+15y-8y =-18x+7y ⑥ 5x-9y+7x-8y=5x+7x-9y-8y =12x-17y ⑦ 10a+b-4a+2b-5=10a-4a+b+2b-5 =6a+3b-5 ⑧ -3a-5b+8-6a+14b =-3a-6a-5b+14b+8 =-9a+9b+8 ⑨ 5x+6y-12-2x+9y+4 =5x-2x+6y+9y-12+4 =3x+15y-8 ⑩ -6x+y+2-6x-13-y =-6x-6x+y-y+2-13 =-12x-11 ⑪ 3a-6b-2a+4b+3c =3a-2a-6b+4b+3c =a-2b+3c ⑫ -8a-3b-8c-7b+14c+5a =-8a+5a-3b-7b-8c+14c =-3a-10b+6c ⑬ -8x+4y+4y-4z-8x =-8x-8x+4y+4y-4z =-16x+8y-4z ⑭ 11x-2y-6z-7x+7y-5z =11x-7x-2y+7y-6z-5z =4x+5y-11z ⑮ 5x2 +9x+5-12x2 -9x =5x2-12x2+9x-9x+5 =-7x2+5 � -x2 +7x-3+7x+9x2 =-x2 +9x2 +7x+7x-3 =8x2+14x-3 � 11x2+2x+3+4x-6-9x2 =11x2 -9x2 +2x+4x+3-6 =2x2 +6x-3 � -12x2-7x-13+7x2-5x+9 =-12x2+7x2-7x-5x-13+9 =-5x2 -12x-4

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## K-4

### 정답및풀이

① -a ② 5x+ ③ - a- b ④ - y+7 ⑤ - a+ x+10 ⑥ 8b-13y ⑦ a- b- c ⑧ -7a2-6a ⑨ 2.9x2+3.4x ⑩ - y2+ y -⑪ ab ⑫ - xy ⑬ ab- xy ⑭ - ab+3xy 2 5 9 1 3 9 10 35 12 9 8 1 3 13 20 3 2 17 6 1 8 2 15 7 12 5 4 11 2 17 4 1 3 17 12 <풀이> ※ 답을 대분수로 고치지 않고 가분수로 쓴다. ① 2a- a-&- a*=2a- a+ a =- a=-a ② -4x+ +9x+ =-4x+9x+ + =5x+ ③ a-2b+ b-3b- a = a- a-2b+ b-3b =- a- b=- a- b ④ -5y+7- y=-5y- y+7=- y+7 ⑤ -a- x+10- a+ x =-a- a- x+ x+10 =- a+ x+10 ⑥ 14b-6y-7y-6b=14b-6b-6y-7y =8b-13y ⑦ - a+ b+ a-3c+ c- b =- a+ a+ b- b-3c+ c = a- b-17c 6 1 8 2 15 1 6 2 8 1 8 5 15 3 15 1 4 1 6 1 3 1 8 1 5 7 12 5 4 9 12 2 12 1 4 3 4 1 4 1 6 11 2 1 2 1 2 17 4 1 3 17 4 2 6 3 4 5 6 3 6 5 6 3 4 1 2 17 12 9 12 8 12 3 4 2 3 3 3 1 3 10 3 1 3 10 3 ⑧ 4a2-13a-11a2+7a=4a2-11a2-13a+7a =-7a2 -6a ⑨ -1.6x2 -0.8x+7x2 +4.2x-2.5x2 =-1.6x2+7x2-2.5x2-0.8x+4.2x =2.9x2+3.4x ⑩ - y2+ y- - + y2+ y =- y2+ y2+ y+ y -=- y2 + y- =- y2 + y -⑪ ab- ab= ab- ab= ab ⑫ - xy+ xy- xy =- xy+ xy- xy=- xy ⑬ ab- xy- ab= ab- ab- xy = ab- xy ⑭ - ab+2xy+ ab- xy =- ab+ ab+2xy- xy =- ab+3xy 2 5 9 1 2 7 9 12 9 1 2 7 9 4 3 1 3 9 10 1 3 16 10 25 10 8 5 1 3 5 2 35 12 20 12 15 12 30 12 5 3 5 4 5 2 9 8 6 8 15 8 3 4 15 8 1 3 13 20 3 2 2 6 13 20 9 6 1 6 1 6 5 20 8 20 5 6 14 6 1 4 5 6 1 6 1 6 2 5 7 3 ① 8x+5y ② 8x+3y ③ 2x+5y ④ 2x+3y ⑤ 8x-3y ⑥ 8x-5y ⑦ 2x-3y ⑧ 2x-5y ⑨ -2x+5y ⑩ -2x+3y ⑪ -8x+5y ⑫ -8x+3y ⑬ -2x-3y ⑭ -2x-5y ⑮ -8x-3y � -8x-5y <풀이> ※ 괄호 앞이 +일 때, +(�+▲)=�+▲, +(�-▲)=�-▲ +(-�+▲)=-�+▲, +(-�-▲)=-�-▲ 임을 이해하고 문제를 풀도록 한다. ① (5x+4y)+(3x+y)=5x+4y+3x+y =8x+5y ② (5x+4y)+(3x-y)=5x+4y+3x-y =8x+3y

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③ (5x+4y)+(-3x+y)=5x+4y-3x+y =2x+5y ④ (5x+4y)+(-3x-y)=5x+4y-3x-y =2x+3y ⑤ (5x-4y)+(3x+y)=5x-4y+3x+y =8x-3y ⑥ (5x-4y)+(3x-y)=5x-4y+3x-y =8x-5y ⑦ (5x-4y)+(-3x+y)=5x-4y-3x+y =2x-3y ⑧ (5x-4y)+(-3x-y)=5x-4y-3x-y =2x-5y ⑨ (-5x+4y)+(3x+y)=-5x+4y+3x+y =-2x+5y ⑩ (-5x+4y)+(3x-y)=-5x+4y+3x-y =-2x+3y ⑪ (-5x+4y)+(-3x+y)=-5x+4y-3x+y =-8x+5y ⑫ (-5x+4y)+(-3x-y)=-5x+4y-3x-y =-8x+3y ⑬ (-5x-4y)+(3x+y)=-5x-4y+3x+y =-2x-3y ⑭ (-5x-4y)+(3x-y)=-5x-4y+3x-y =-2x-5y ⑮ (-5x-4y)+(-3x+y)=-5x-4y-3x+y =-8x-3y � (-5x-4y)+(-3x-y)=-5x-4y-3x-y =-8x-5y ① 6a+9b ② 4a-2b ③ 3a-7b ④ -8a-7b ⑤ -6a+4b ⑥ 5a-10b ⑦ 2a+6b ⑧ -3a+b ⑨x+8y-3 ⑩ 2a-4 ⑪ 6x-9y+10z ⑫-5a-7b-2c ⑬ -5x-10z ⑭ 7b ⑮-7a2+6a+5 � -9x2+8y2 <풀이> ① (4a+4b)+(2a+5b)=4a+4b+2a+5b =6a+9b ② (-4a+6b)+(8a-8b)=-4a+6b+8a-8b =4a-2b ③ (9a-b)+(-6a-6b)=9a-b-6a-6b =3a-7b ④ (-3a-8b)+(-5a+b)=-3a-8b-5a+b =-8a-7b ⑤ (3a+2b)+(-9a+2b)=3a+2b-9a+2b =-6a+4b ⑥ (a-7b)+(4a-3b)=a-7b+4a-3b =5a-10b ⑦ (-3a-b)+(5a+7b)=-3a-b+5a+7b =2a+6b ⑧ (-2a+9b)+(-a-8b)=-2a+9b-a-8b =-3a+b ⑨ (8x+2y+2)+(-7x+6y-5) =8x+2y+2-7x+6y-5 =x+8y-3 ⑩ (a+5b-3)+(a-5b-1) =a+5b-3+a-5b-1 =2a-4 ⑪ (3x-6y+6z)+(3x-3y+4z) =3x-6y+6z+3x-3y+4z =6x-9y+10z ⑫ (3a-4b-6c)+(-8a-3b+4c) =3a-4b-6c-8a-3b+4c =-5a-7b-2c ⑬ (-4x+9y-2z)+(-x-9y-8z) =-4x+9y-2z-x-9y-8z =-5x-10z ⑭ (-7a+5b+2c)+(7a+2b-2c) =-7a+5b+2c+7a+2b-2c=7b ⑮ (-9a2-2a+3)+(2a2+8a+2) =-9a2 -2a+3+2a2 +8a+2=-7a2 +6a+5 � (-7x2 -4xy-y2 )+(-2x2 +4xy+9y2 ) =-7x2-4xy-y2-2x2+4xy+9y2 =-9x2+8y2 ① -, - ② -, + ③ +, -④ +, + ⑤ -, - ⑥ -, + ⑦ +, - ⑧ +, + ⑨ , -⑩ -, + ⑪ +, - ⑫ +, + ⑬ 2x-4 ⑭ 2x+4 ⑮ 8x-4 � 8x+4 � -8x-4 � -8x+4 � -2x-4 � -2x+4 � -3x+1 � -3x+9 � 3x-9 � 3x-1 <풀이> ※ 괄호 앞이 -일 때, -(�+▲)=-�-▲, -(-�+▲)=�-▲ -(�-▲)=-�+▲, -(-�-▲)=�+▲ 임을 이해하고 문제를 풀도록 한다.

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## K-4

### 정답및풀이

①x-(y+z)=x-y-z ②x-(y-z)=x-y+z ③x-(-y+z)=x+y-z ④x-(-y-z)=x+y+z ⑤ -x-(y+z)=-x-y-z ⑥ -x-(y-z)=-x-y+z ⑦ -x-(-y+z)=-x+y-z ⑧ -x-(-y-z)=-x+y+z ⑨ 2x-(y+3z)=2x-y-3z ⑩ 2x-(y-3z)=2x-y+3z ⑪ -2x-(-y+3z)=-2x+y-3z ⑫ -2x-(-y-3z)=-2x+y+3z ⑬ 5x-(3x+4)=5x-3x-4=2x-4 ⑭ 5x-(3x-4)=5x-3x+4=2x+4 ⑮ 5x-(-3x+4)=5x+3x-4=8x-4 � 5x-(-3x-4)=5x+3x+4=8x+4 � -5x-(3x+4)=-5x-3x-4=-8x-4 � -5x-(3x-4)=-5x-3x+4=-8x+4 � -5x-(-3x+4)=-5x+3x-4=-2x-4 � -5x-(-3x-4)=-5x+3x+4=-2x+4 � 5-(3x+4)=5-3x-4=-3x+1 � 5-(3x-4)=5-3x+4=-3x+9 � -5-(-3x+4)=-5+3x-4=3x-9 � -5-(-3x-4)=-5+3x+4=3x-1 ① -a-3b ② -a+3b ③a-3b ④a+3b ⑤ -a-9b ⑥ 9a-3b ⑦ -9a+3b ⑧a+9b ⑨ 2x+4y ⑩ -8a-5b ⑪ 7a-3x ⑫b-6y ⑬ -5x+y-3 ⑭ 9a-3b-5c ⑮ 5x+3y-6 � -7a-2b-4c <풀이> ① (4a+3b)-(5a+6b)=4a+3b-5a-6b =-a-3b ② (4a-3b)-(5a-6b)=4a-3b-5a+6b =-a+3b ③ (-4a+3b)-(-5a+6b)=-4a+3b+5a-6b =a-3b ④ (-4a-3b)-(-5a-6b)=-4a-3b+5a+6b =a+3b ⑤ (4a-3b)-(5a+6b)=4a-3b-5a-6b =-a-9b ⑥ (4a+3b)-(-5a+6b)=4a+3b+5a-6b =9a-3b ⑦ (-4a-3b)-(5a-6b)=-4a-3b-5a+6b =-9a+3b ⑧ (-4a+3b)-(-5a-6b)=-4a+3b+5a+6b =a+9b ⑨ (-7x+2y)-(-9x-2y)=-7x+2y+9x+2y =2x+4y ⑩ (-5a-6b)-(3a-b)=-5a-6b-3a+b =-8a-5b ⑪ (3a+5x)-(-4a+8x)=3a+5x+4a-8x =7a-3x ⑫ (4b-4y)-(3b+2y)=4b-4y-3b-2y =b-6y ⑬ (-2x+6y)-(3x+5y+3) =-2x+6y-3x-5y-3=-5x+y-3 ⑭ (8a+4b-5c)-(-a+7b)=8a+4b-5c+a-7b =9a-3b-5c ⑮ (-2x+y-9)-(-7x-2y-3) =-2x+y-9+7x+2y+3 =5x+3y-6 � (-5a-3b+4c)-(2a-b+8c) =-5a-3b+4c-2a+b-8c =-7a-2b-4c ① 8a-3b ② 6a+7b ③ -3x-y ④ 5x-9y ⑤ -8x2+2x ⑥ 4x2+8x ⑦ -2x2+5x+4 ⑧ -2x2-13x-4 ⑨ 7a-13 ⑩ 11a+3 ⑪ -7x+13 ⑫ -11x-3 ⑬ 11a+5b-8 ⑭ 3a+5b+2 ⑮ -3x-11y+2 � -15x+5y+2 <풀이> ① (7a+2b)+(a-5b)=7a+2b+a-5b=8a-3b ② (7a+2b)-(a-5b)=7a+2b-a+5b=6a+7b ③ (x-5y)+(-4x+4y)=x-5y-4x+4y =-3x-y ④ (x-5y)-(-4x+4y)=x-5y+4x-4y =5x-9y ⑤ (-2x2 +5x)+(-6x2 -3x)=-2x2 +5x-6x2 -3x =-8x2 +2x ⑥ (-2x2+5x)-(-6x2-3x)=-2x2+5x+6x2+3x =4x2+8x ⑦ (-2x2 -4x)+(9x+4)=-2x2 -4x+9x+4 =-2x2 +5x+4 ⑧ (-2x2-4x)-(9x+4)=-2x2-4x-9x-4 =-2x2-13x-4

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⑨ (9a-5)+(-2a-8)=9a-5-2a-8=7a-13 ⑩ (9a-5)-(-2a-8)=9a-5+2a+8=11a+3 ⑪ (-9x+5)+(2x+8)=-9x+5+2x+8 =-7x+13 ⑫ (-9x+5)-(2x+8)=-9x+5-2x-8 =-11x-3 ⑬ (7a+5b-3)+(4a-5)=7a+5b-3+4a-5 =11a+5b-8 ⑭ (7a+5b-3)-(4a-5)=7a+5b-3-4a+5 =3a+5b+2 ⑮ (-9x-3y+2)+(-8y+6x) =-9x-3y+2-8y+6x =-3x-11y+2 � (-9x-3y+2)-(-8y+6x) =-9x-3y+2+8y-6x =-15x+5y+2 ① 4x+9 ② -3x+7y+5 ③ 6a-8b-2c ④ -6x+y+5z ⑤ 2.5x2 +xy-4.7y2 ⑥ - a2 - a ⑦a-3b-1 ⑧ -x+2y+4 ⑨ 3a-5b ⑩ -4y+9z ⑪ - a+4b- c ⑫ - x2+ x+3 7 5 2 8 3 7 2 3 2 5 3 13 5 <풀이> ※ 답은 대분수가 아닌 가분수로 쓴다. ① (7x+1)+(-3x+8)=7x+1-3x+8=4x+9 ② (-2x+4y+5)-(x-3y)=-2x+4y+5-x+3y =-3x+7y+5 ③ (3a-2b-4c)-(-3a+6b-2c) =3a-2b-4c+3a-6b+2c =6a-8b-2c ④ (-8x-z)+(2x+y+6z)=-8x-z+2x+y+6z =-6x+y+5z ⑤ (0.9x2 +xy+0.3y2 )-(-1.6x2 +5y2 ) =0.9x2+xy+0.3y2+1.6x2-5y2 =2.5x2+xy-4.7y2 ⑥ &-3a2- a*+& a2- a* =-3a2- a+ a2- a=- a2- a ⑦ (a+3b-9)+(-6b+8)=a+3b-9-6b+8 =a-3b-1 5 3 13 5 4 3 2 5 1 3 4 3 2 5 1 3 ⑧ (-2x-5)-(-x-2y-9)=-2x-5+x+2y+9 =-x+2y+4 ⑨ (8a-3b)-(5a+2b)=8a-3b-5a-2b =3a-5b ⑩ (-6x-3y+2z)+(6x-y+7z) =-6x-3y+2z+6x-y+7z=-4y+9z ⑪ &- a+ b*+&-a+ b- c* =- a+ b-a+ b- c =- a+4b- c ⑫ & x2+2x- *-&3x2- x-1* = x2+2x- -3x2+ x+1 =- x2 + x+3 7 5 2 8 3 1 2 4 7 1 3 1 2 4 7 1 3 7 2 3 2 7 2 5 2 3 2 1 2 7 2 5 2 3 2 1 2 ① 9x+y-2 ② 6x-4y+8 ③ -7x+3 ④ -9x-5y ⑤ -9a+2b ⑥ 2a-5b ⑦ 2b+6c ⑧ 7a-8b-3c ⑨ -5x2 -3x-4 ⑩ -4a2 +4a+5 ⑪ x+ y ⑫ - a+5b 4 13 6 13 9 7 8 <풀이> ※ 답은 대분수가 아닌 가분수로 쓴다. ① (4x+7y+3)+(5x-6y-5) =4x+7y+3+5x-6y-5 =9x+y-2 ② (5x-6y+4)-(-x-2y-4) =5x-6y+4+x+2y+4 =6x-4y+8 ③ (-2x+8y-4)-(5x+8y-7) =-2x+8y-4-5x-8y+7 =-7x+3 ④ (-8x-7y+3)+(-x+2y-3) =-8x-7y+3-x+2y-3 =-9x-5y ⑤ (-2a-5b)-(3a+2b)+(-4a+9b) =-2a-5b-3a-2b-4a+9b =-9a+2b

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## K-4

### 정답및풀이

⑥ -(a-5b)+(-4a-4b)-(-7a+6b) =-a+5b-4a-4b+7a-6b =2a-5b ⑦ (4a-6b+9c)-(4a-8b+3c) =4a-6b+9c-4a+8b-3c =2b+6c ⑧ (3a-b-4c)-(-4a+7b-c) =3a-b-4c+4a-7b+c =7a-8b-3c ⑨ -2x2 -(2x+4)+(-3x2 -x) =-2x2 -2x-4-3x2 -x =-5x2-3x-4 ⑩ (-2a2+5a)-(2a2+3)-(a-8) =-2a2 +5a-2a2 -3-a+8 =-4a2 +4a+5 ⑪ &x+ y*-& x- y*=x+ y- x+ y = x+ y ⑫ &- a+ b*-&- a- b* =- a+ b+ a+ b =- a+ a+ b+ b =- a+5b 4 13 6 3 4 2 4 2 6 15 6 3 4 1 3 1 2 5 2 3 4 1 3 1 2 5 2 13 9 7 8 8 9 1 8 5 9 8 9 1 8 5 9 ① 6a-7 ② -7x+8y ③ -5a+4b-9c ④ x- y+5z ⑤ - a+ ⑥ a+ b- c ⑦ 9a-2b ⑧ -4x+5y ⑨ -4a-6b ⑩ 6x+y ⑪ 8a-3b-5c ⑫ -2x+y-8z ⑬ 4a-5b+7 ⑭ -3x+9y+2z 4 3 1 5 1 7 25 3 5 12 3 2 5 6 <풀이> ① (12a-16)-(6a-9) =12a-16-6a+9 =6a-7 ② (-5x+6y)+(5x-7y)-(7x-9y) =-5x+6y+5x-7y-7x+9y =-7x+8y ③ (-11a-6b)-(-10b+16c)+(6a+7c) =-11a-6b+10b-16c+6a+7c =-5a+4b-9c ④ & x- y*-&- x+ y-5z* = x- y+ x- y+5z = x+ x- y- y+5z = x- y+5z ⑤ &- a+ b+10*+& a- b- * =- a+ b+10+ a- b -=- a+ a+ b- b +10-=- a+ ⑥ (a+2b-c)-&- a+2b+c*-&a- b- c* =a+2b-c+ a-2b-c-a+ b+ c = a+ b- c ※ 다음 풀이는 암산이 안 되는 학생들을 위하 여 써 놓은 것이므로, 계산 과정을 참조하여 답 만 쓰도록 한다. ⑦ (5a-7b)+(4a+5b)=5a-7b+4a+5b =9a-2b ⑧ (-9x+6y)-(-5x+y)=-9x+6y+5x-y =-4x+5y ⑨ (-a-4b)-(3a+2b)=-a-4b-3a-2b =-4a-6b ⑩ (9x-5y)+(6y-3x)=9x-5y+6y-3x =6x+y ⑪ (5a+6b)+(3a-9b-5c) =5a+6b+3a-9b-5c =8a-3b-5c ⑫ (-3x+y-6z)-(2z-x) =-3x+y-6z-2z+x =-2x+y-8z ⑬ (6a-8b+4)+(-2a+3b+3) =6a-8b+4-2a+3b+3 =4a-5b+7 ⑭ (-x+7y-4z)-(-2y-6z+2x) =-x+7y-4z+2y+6z-2x =-3x+9y+2z 4 3 1 5 1 7 2 3 1 5 1 7 2 3 1 5 1 7 25 3 5 12 5 3 6 5 6 5 10 12 15 12 5 3 6 5 5 6 6 5 5 4 5 3 6 5 5 6 6 5 5 4 3 2 5 6 1 6 8 6 2 6 3 6 1 6 1 3 4 3 1 2 1 6 1 3 4 3 1 2

(27)

<풀이> ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ � -5x+2y+3z +)≥ 3x+4y+4z � -5x+2y+3z -)≥ -3x -4y-4z -3a+7b-3c +)≥ -a -2b+4c � -3a+7b-3c -)≥ a+2b-4c 3x-2y-6 +)≥ x+4y-2 4x+2y-8 � 3x-2y-6 -)≥-x-4y+2 4a-2b-7 +)≥ -3a -3b+1 � 4a-2b-7 -)≥3a+3b-1 -5x+2y+3z +)≥ -3x -4y-4z -3a+7b-3c +)≥a+2b-4c -2a+9b-7c 3x-2y-6 +)≥-x-4y+2 2x-6y-4 4a-2b-7 +)≥3a+3b-1 7a+ b-8 -3a-4b +)≥5a+4b 2a+3b � -3a-4b -)≥-5a -4b -x+6y +)≥-7x-6y -8x-5y � -x+6y -)≥7x+6y 2a-1 +)≥5a-6 7a-7 � 2a-1 －)≥ -5a+6 x+3 +)≥-5x+6 -4x+9 � x+3 －)≥5x-6 -3a-4b +)≥-5a-4b -8a-5b -x+6y +)≥7x+6y 6x+7y 2a-1 +)≥-5a+6 -3a+5 x+3 +)≥5x-6 6x-3 ① 7a-2 ② -3x+y+7 ③ -7a2-5ab-6b2 ④ 2x+4y-9z ⑤ -6x-5y ⑥ 5a2 ⑦ 8y+4z ⑧ -a2+9b2 ⑨ 4a+7b-4 ⑩ -14x2 ⑪ 9b ⑫ -3a+c ⑬ - x2 -4xy+ y2 ⑭ - x+ ⑮ x2 +5x � -11a+ b-1c 6 8 9 8 5 1 3 5 2 4 5 8 7 <풀이> ※ 답은 대분수가 아닌 가분수로 쓴다. ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ -5x2-4xy+8y2 +)≥ -9x2 +4xy-8y2 � -5x2-4xy+8y2 -)≥ 9x2 -4xy+8y2 4a+5b-7 +)≥ 2b+3 4a+7b-4 5a2-3ab+2b2 +)≥ -6a2+3ab+7b2 -9x+5y+4z +)≥ 9x+3y+4z � -9x+5y+4z -)≥ -9x -3y+4z -6a+2 +)≥5a2 +6a-2 5a2+6a-2 -2x-3y +)≥-4x-2y -6x-5y � -2x-3y -)≥4x+2y -2x+2y-6z +)≥ 4x+2y -3z � -2x+2y-6z -)≥ -4x -2y+3z -9ab+2b2 +)≥-7a2 +4ab -8b2 3x-4y+7 +)≥ -6x+5y+7 � 3x-4y+7 -)≥6x-5y+7 3a+7 +)≥4a-9 7a-2 ① 6x-3 ② -3a+5 ③ 6x+7y ④ -8a-5b ⑤ -4x+9 ⑥ 7a-7 ⑦ -8x-5y ⑧ 2a+3b ⑨ 7a+b-8 ⑩ 2x-6y-4 ⑪ -2a+9b-7c ⑫ -8x-2y-z ⑬a-5b-6 ⑭ 4x+2y-8 ⑮ -4a+5b+c � -2x+6y+7z

(28)

⑪ ⑫ ⑬ ⑭ ⑮ � � � � 5a-7b+c +)≥-8a+7b+c -3a+7b+c -4a+4b +)≥4a+5b 9b � -4a+4b -)≥-4a-5b

## K-4

### 정답및풀이

- x2 -4xy+ 2y2 -} -x2 +4xy+ 6y2 5 3 7 5 7 - x 2 -4xy+ 2y2 +} - x2 -4xy- 6y2 5 3 7 5 7 x- 2 +} -3x+ - x+1 3 5 2 7 3 1 2 x2+5x --≥ x} 2-5x-2 7 1 5 2 7 9 5 x 2+5x -+} - x2+5x+ x2+5x+ 8 5 2 7 1 5 2 7 9 5 -3a+ b+ c +} -8a- b-2c 3 7 9 1 2 5 3 -3a+ b+ c +} -8a- b- c -11a+ b-1c 6 8 9 4 6 7 9 3 6 15 9 ① 6x+9y ② 6x-9y ③ -6x+9y ④ -6x-9y ⑤ 4x+6y+8z ⑥ 4x-6y+8z ⑦ -4x+6y-8z ⑧ -4x-6y+8z ⑨ 3x+ y ⑩ -3x- y ⑪ -6x-9y ⑫ -6x+9y ⑬ 6x-9y ⑭ 6x+9y ⑮ -4x-6y+8z � -4x+6y+8z � 4x-6y-8z � 4x+6y+8z � - x+6y �3x-6y 2 3 2 3 2 3 2 <풀이> ※ 다음 풀이는 암산이 안 되는 학생들을 위하 여 써 놓은 것이므로, 계산 과정을 참조하여 답 만 쓰도록 한다. ① 3(2x+3y)=3×2x+3×3y=6x+9y ② 3(2x-3y)=3×2x+3×(-3y)=6x-9y ③ 3(-2x+3y)=3×(-2x)+3×3y=-6x+9y ④ 3(-2x-3y)=3×(-2x)+3×(-3y) =-6x-9y ⑤ 2(2x+3y+4z)=2×2x+2×3y+2×4z =4x+6y+8z ⑥ 2(2x-3y+4z)=2×2x+2×(-3y)+2×4z =4x-6y+8z ⑦ 2(-2x+3y-4z) =2×(-2x)+2×3y+2×(-4z) =-4x+6y-8z ⑧ 2(-2x-3y+4z) =2×(-2x)+2×(-3y)+2×4z =-4x-6y+8z ⑨ 9& x+ y*=9× x+9× y=3x+ y ⑩ 9&- x- y*=9×&- x*+9×&- y*

=-3x- y ⑪ -3(2x+3y)=-3×2x-3×3y=-6x-9y ⑫ -3(2x-3y)=-3×2x-3×(-3y)=-6x+9y ⑬ -3(-2x+3y)=-3×(-2x)-3×3y=6x-9y ⑭ -3(-2x-3y)=-3×(-2x)-3×(-3y) =6x+9y ⑮ -2(2x+3y-4z)=-2×2x-2×3y-2×(-4z) =-4x-6y+8z � -2(2x-3y-4z) =-2×2x-2×(-3y)-2×(-4z) =-4x+6y+8z � -2(-2x+3y+4z) =-2×(-2x)-2×3y-2×4z =4x-6y-8z � -2(-2x-3y-4z) =-2×(-2x)-2×(-3y)-2×(-4z) =4x+6y+8z � - (2x-8y)=- ×2x- ×(-8y) =- x+6y � - (-2x+8y)=- ×(-2x)- ×8y =3x-6y 2 3 4 3 4 3 4 3 2 3 4 3 4 3 4 3 2 1 6 1 3 1 6 1 3 3 2 1 6 1 3 1 6 1 3

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① 5a-6b ② -5a-4b ③ -3a-8b ④ 10a-9b ⑤ -9x+12y ⑥ -5x+10y ⑦ 7x+3y ⑧ 4x+6y ⑨ 13x+16 ⑩ 13x-4 ⑪ 5x+16 ⑫ 5x-4 ⑬ 5a-16 ⑭ 5a+4 ⑮ 13a-16 � 13a+4 <풀이> ① 2a+3(a-2b)=2a+3a-6b=5a-6b ② 3a+4(-2a-b)=3a-8a-4b=-5a-4b ③a-2(2a+4b)=a-4a-8b=-3a-8b ④ 4a-3(-2a+3b)=4a+6a-9b=10a-9b ⑤ -x+4(-2x+3y)=-x-8x+12y =-9x+12y ⑥ -3x-2(x-5y)=-3x-2x+10y =-5x+10y ⑦ -2x+3(3x+y)=-2x+9x+3y=7x+3y ⑧ -4x-2(-4x-3y)=-4x+8x+6y =4x+6y ⑨ 3(3x+2)+2(2x+5)=9x+6+4x+10 =13x+16 ⑩ 3(3x+2)+2(2x-5)=9x+6+4x-10 =13x-4 ⑪ 3(3x+2)+2(-2x+5)=9x+6-4x+10 =5x+16 ⑫ 3(3x+2)+2(-2x-5)=9x+6-4x-10 =5x-4 ⑬ 3(3a-2)-2(2a+5)=9a-6-4a-10 =5a-16 ⑭ 3(3a-2)-2(2a-5)=9a-6-4a+10 =5a+4 ⑮ 3(3a-2)-2(-2a+5)=9a-6+4a-10 =13a-16 � 3(3a-2)-2(-2a-5)=9a-6+4a+10 =13a+4 ① -5a+16 ② -5a-4 ③ -13a+16 ④ -13a-4 ⑤ -13x-16 ⑥ -13x+4 ⑦ -5x-16 ⑧ -5x+4 ⑨ 8a+8 ⑩ -11x-12 ⑪ -3a+20 ⑫ 2x-14 ⑬ 8a-24 ⑭ -x+9 ⑮ -a+4 � -x-4 <풀이> ① -3(3a-2)+2(2a+5)=-9a+6+4a+10 =-5a+16 ② -3(3a-2)+2(2a-5)=-9a+6+4a-10 =-5a-4 ③ -3(3a-2)+2(-2a+5)=-9a+6-4a+10 =-13a+16 ④ -3(3a-2)+2(-2a-5)=-9a+6-4a-10 =-13a-4 ⑤ -3(3x+2)-2(2x+5)=-9x-6-4x-10 =-13x-16 ⑥ -3(3x+2)-2(2x-5)=-9x-6-4x+10 =-13x+4 ⑦ -3(3x+2)-2(-2x+5)=-9x-6+4x-10 =-5x-16 ⑧ -3(3x+2)-2(-2x-5)=-9x-6+4x+10 =-5x+4 ⑨ 2(a-2)+3(2a+4)=2a-4+6a+12 =8a+8 ⑩ -(7x-4)+4(-x-4)=-7x+4-4x-16 =-11x-12 ⑪ 3(-3a+5)-(-6a-5)=-9a+15+6a+5 =-3a+20 ⑫ -4(-2x+3)-2(3x+1)=8x-12-6x-2 =2x-14 ⑬ 4&- a-3*-9&-a+ *=-a-12+9a-12 =8a-24 ⑭ -6&- - *+10&- + *=x+4-2x+5 =-x+9 ⑮ 2(a-2)-(-3a+1)+3(-2a+3) =2a-4+3a-1-6a+9 =-a+4 � -3(x-2)+4(2x-3)-2(3x-1) =-3x+6+8x-12-6x+2 =-x-4 1 2 x 5 2 3 x 6 4 3 1 4 ① 8a-10b ② -x+2 ③ -8a+15 ④ -2x-3y+ ⑤ 6a+2 ⑥ -x-14y ⑦ 7a-20b ⑧ -6y+18 ⑨ 2b-2 ⑩y+1 ⑪ -18a-6 ⑫- x+ y ⑬ 8a+2b ⑭ 3x 10 3 1 2 4 3

(30)

## K-4

### 정답및풀이

<풀이> ※ ①~⑧까지는 가능하면 암산을 하여 답만 쓰 도록 한다. ① 2(4a-5b)=2×4a+2×(-5b) =8a-10b ② (-2x+4)× =(-2x)× +4× =-x+2 ③ & a- *×(-12)= a×(-12)- ×(-12) =-8a+15 ④ - (6x+9y-4)=- ×6x- ×9y- ×(-4) =-2x-3y+ ⑤ -2(3a-5)+4(3a-2)=-6a+10+12a-8 =6a+2 ⑥ 5(x-y)-3(2x+3y)=5x-5y-6x-9y =-x-14y ⑦ -3(-a+4b)+2(2a-4b)=3a-12b+4a-8b =7a-20b ⑧ (5y+6)-2(4y-3)+3(-y+2) =5y+6-8y+6-3y+6 =-6y+18 ⑨ b+ (b-4)= b+ b-2 =2b-2 ⑩ (y+3)+ (6y-2)= y+ + y -=y+1 ⑪ 4&- a+1*-6&2a+ *=-6a+4-12a-10 =-18a-6 ⑫ - (-6x-y)+3&- x+y* =2x+ y- x+3y =- x+ y ⑬ -8&- a+ b*- (-4a-6b) =2a-7b+6a+9b =8a+2b ⑭ 2x- (6x-8)- (-5x+4) =2x- x+2+ x-2 =3x 5 2 3 2 1 2 1 4 3 2 7 8 1 4 10 3 1 2 5 2 1 3 5 6 1 3 5 3 3 2 1 5 3 5 6 5 2 5 1 10 2 5 1 2 3 2 1 2 3 2 4 3 1 3 1 3 1 3 1 3 5 4 2 3 5 4 2 3 1 2 1 2 1 2 ① & x+ * ② & x- * ③ &- x+ * ④ &- x- * ⑤ &- x+ * ⑥ & x+ * ⑦ & x- * ⑧ & x+ * ⑨ & x+ * ⑩ & x+ * ⑪ & x+ * ⑫ &- x- *7 9 2 9 -2x-7 9 1 5 8 5 8x+1 5 3 8 7 8 7x+3 8 8 3 2 3 2x+8 3 9 2 7 2 7x+9 2 3 7 8 7 8x-3 7 3 4 5 4 5x+3 4 5 3 8 3 -8x+5 3 7 5 6 5 -6x-7 5 3 7 2 7 -2x+3 7 9 7 4 7 4x-9 7 1 6 5 6 5x+1 6 <풀이> ① + = = & x+ * ② + = = & x- * ③ - = = &- x+ * ④ - = = &- x- * ⑤ - + = = &- x+ * ⑥ - + = = & x+ * ⑦ - - = = & x- * ⑧ - - = = & x+ *9 2 7 2 7x+9 2 -(-9x-4)-(2x-5) 2 2x-5 2 -9x-4 2 3 7 8 7 8x-3 7 -(-5x+5)-(-3x-2) 7 -3x-2 7 -5x+5 7 3 4 5 4 5x+3 4 -(x-2)+(6x+1) 4 6x+1 4 x-2 4 5 3 8 3 -8x+5 3 -(4x+2)+(-4x+7) 3 -4x+7 3 4x+2 3 7 5 6 5 -6x-7 5 (-3x-5)-(3x+2) 5 3x+2 5 -3x-5 5 3 7 2 7 -2x+3 7 (-4x+8)-(-2x+5) 7 -2x+5 7 -4x+8 7 9 7 4 7 4x-9 7 (5x-6)+(-x-3) 7 -x-3 7 5x-6 7 1 6 5 6 5x+1 6 (x+4)+(4x-3) 6 4x-3 6 x+4 6

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⑨ + = = & x+ * ⑩ - = = & x+ * ⑪ - + = = & x+ * ⑫ - - = = &- x- *7 9 2 9 -2x-7 9 -(4x+6)-(-2x+1) 9 -2x+1 9 4x+6 9 1 5 8 5 8x+1 5 -(-x-4)+(7x-3) 5 7x-3 5 -x-4 5 3 8 7 8 7x+3 8 (3x-2)-(-4x-5) 8 -4x-5 8 3x-2 8 8 3 2 3 2x+8 3 (-6x+1)+(8x+7) 3 8x+7 3 -6x+1 3 ① & x+ * ② &- x- * ③ & x- * ④ &- x+ * ⑤ & x+ * ⑥ - x ⑦ & x-1* ⑧ -5 12 13 6 13x-6 6 5 8 4 3 5 6 5x+8 6 13 12 1 6 -2x+13 12 5 6 2 3 4x-5 6 5 4 3 4 -3x-5 4 1 3 5 6 5x+2 6 <풀이> ① + = = = & x+ * ② - = = = &- x- *5 4 3 4 -3x-5 4 -x+3-2x-8 4 (-x+3)-2(x+4) 4 x+4 2 -x+3 4 1 3 5 6 5x+2 6 3x+6+2x-4 6 3(x+2)+2(x-2) 6 x-2 3 x+2 2 ③ - + = = = & x- * ④ - - = = = &- x+ * ⑤ + = = = & x+ * ⑥ - = = =- x ⑦ - + = = = & x-1* ⑧ - - = = =-5 12 6x-3-6x-2 12 -3(-2x+1)-2(3x+1) 12 3x+1 6 -2x+1 4 13 6 13x-6 6 4x+6+9x-12 6 -2(-2x-3)+3(3x-4) 6 3x-4 2 -2x-3 3 5 8 -2x-6-3x+6 8 2(-x-3)-(3x-6) 8 3x-6 8 -x-3 4 4 3 5 6 5x+8 6 -4x+2+9x+6 6 (-4x+2)+3(3x+2) 6 3x+2 2 -4x+2 6 13 12 1 6 -2x+13 12 6x+9-8x+4 12 -3(-2x-3)-4(2x-1) 12 2x-1 3 -2x-3 4 5 6 2 3 4x-5 6 6x-4-2x-1 6 -2(-3x+2)+(-2x-1) 6 -2x-1 6 -3x+2 3 ① & x+ * ② &- x- * ③ &- x+ * ④ ⑤ &- x- * ⑥ & x- * ⑦ & x+ * ⑧ -5x 18 11 6 1 3 2x+11 6 9 8 1 8 x-9 8 8 9 1 3 -3x-8 9 9 10 3 2 1 6 -x+9 6 1 5 7 10 -7x-2 10 1 2 9 4 9x+2 4

(32)

## K-4

### 정답및풀이

<풀이> ① + = = = & x+ * ② - + = = = &- x- * ③ - = = = &- x+ * ④ - - = = = ⑤ - - = = = &- x- * ⑥ - = = = & x- * ⑦ - + = = = & x+ * ⑧ + = = =-5x 18 -2x-12-3x+12 18 2(-x-6)+3(-x+4) 18 -x+4 6 -x-6 9 11 6 1 3 2x+11 6 -6x+9+8x+2 6 -3(2x-3)+2(4x+1) 6 4x+1 3 2x-3 2 9 8 1 8 x-9 8 6x-8-5x-1 8 2(3x-4)-(5x+1) 8 5x+1 8 3x-4 4 8 9 1 3 -3x-8 9 -6x-2+3x-6 9 -(6x+2)-3(-x+2) 9 -x+2 3 6x+2 9 9 10 -4x+6+4x+3 10 -2(2x-3)-(-4x-3) 10 -4x-3 10 2x-3 5 3 2 1 6 -x+9 6 3x+5-4x+4 6 (3x+5)-2(2x-2) 6 2x-2 3 3x+5 6 1 5 7 10 -7x-2 10 -5x-10-2x+8 10 -5(x+2)+2(-x+4) 10 -x+4 5 x+2 2 1 2 9 4 9x+2 4 5x-4+4x+6 4 (5x-4)+2(2x+3) 4 2x+3 2 5x-4 4 ① & x- y* ② &- x+ y* ③ &- x- y* ④ x ⑤ &- x- y* ⑥ &- x+ y* ⑦ - y ⑧ & x+6y* 5 9 10 9x+12y 10 1 24 17 14 3 7 -6x+17y 14 3 20 1 20 -x-3y 20 5 4 7 5 8 15 -8x-21y 15 1 12 13 12 -13x+y 12 4 9 7 9 7x-4y 9 <풀이> ① - = = = & x- y* ② - - = = = &- x+ y* ③ + = = = &- x- y* ④ - + = = = =5x 4 10x 8 8x-4y+2x+4y 8 -4(-2x+y)+(2x+4y) 8 2x+4y 8 -2x+y 2 7 5 8 15 -8x-21y 15 -3x-6y-5x-15y 15 3(-x-2y)+5(-x-3y) 15 -x-3y 3 -x-2y 5 1 12 13 12 -13x+y 12 -4x-2y-9x+3y 12 -2(2x+y)-3(3x-y) 12 3x-y 4 2x+y 6 4 9 7 9 7x-4y 9 6x-3y+x-y 9 3(2x-y)-(-x+y) 9 -x+y 9 2x-y 3

(33)

⑤ - + = = = &- x- y* ⑥ + = = = &- x+ y* ⑦ - -= = =- y ⑧ -= = = & x+6y* 5 9 10 9x+12y 10 -3x+2y+12x+10y 10 (-3x+2y)-2(-6x-5y) 10 -6x-5y 5 -3x+2y 10 1 24 6x+9y-6x-10y 24 -3(-2x-3y)-2(3x+5y) 24 3x+5y 12 -2x-3y 8 17 14 3 7 -6x+17y 14 8x+10y-14x+7y 14 2(4x+5y)+7(-2x+y) 14 -2x+y 2 4x+5y 7 3 20 1 20 -x-3y 20 -5x+5y+4x-8y 20 -5(x-y)+4(x-2y) 20 x-2y 5 x-y 4 ① &- x+ * ② & x+ * ③ - x ④ & x- y* ⑤ &- x+ * ⑥ & x- * ⑦ &- x- y* ⑧ & x+1y* 30 1 6 5x+y 30 1 4 1 6 -2x-3y 12 11 30 1 30 x-11 30 1 6 5 6 -5x+1 6 9 8 3 4 6x-9y 8 19 18 1 5 9 10 9x+2 10 5 6 5 3 -10x+5 6 <풀이> ① - + = = = &- x+ * ② + = = = & x+ * ③ - -= = =- x ④ - = = = & x- y* ⑤ - = = = &- x+ * ⑥ - - = = = & x- * ⑦ + = = = &- x-1y* 4 1 6 -2x-3y 12 6x-15y-8x+12y 12 3(2x-5y)+4(-2x+3y) 12 -2x+3y 3 2x-5y 4 11 30 1 30 x-11 30 6x-6-5x-5 30 -6(-x+1)-5(x+1) 30 x+1 6 -x+1 5 1 6 5 6 -5x+1 6 -3x-6-2x+7 6 3(-x-2)-(2x-7) 6 2x-7 6 -x-2 2 9 8 3 4 6x-9y 8 8x-6y-2x-3y 8 2(4x-3y)-(2x+3y) 8 2x+3y 8 4x-3y 4 19 18 -10x-12y-9x+12y 18 -2(5x+6y)-3(3x-4y) 18 3x-4y 6 5x+6y 9 1 5 9 10 9x+2 10 15x+10-6x-8 10 5(3x+2)+2(-3x-4) 10 -3x-4 5 3x+2 2 5 6 5 3 -10x+5 6 -4x+1-6x+4 6 -(4x-1)+2(-3x+2) 6 -3x+2 3 4x-1 6

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## K-4

### 정답및풀이

⑧ - + = = = & x+1y* 30 1 6 5x+y 30 8x+10y-3x-9y 30 -2(-4x-5y)+3(-x-3y) 30 -x-3y 10 -4x-5y 15 ① &- x-2* ② &- a+ b* ③ & b+ * ④ & x+ y* ⑤ ⑥ x ⑦ &- y+ * ⑧ &-a-1b* 2 -2a-b 2 5 3 5 2 -15y+10 6 5 6 2 3 5 3 4 3 4x+5y 3 4 5 2 3 10b+12 15 11 24 1 2 -12a+11b 24 3 4 -3x-8 4 <풀이> ① - = = = &- x-2* ② - - = = = &- a+ b* ③ - + = = = & b+ *4 5 2 3 10b+12 15 15b-3-5b+15 15 -3(-5b+1)+5(-b+3) 15 -b+3 3 -5b+1 5 11 24 1 2 -12a+11b 24 -6a+9b-6a+2b 24 -3(2a-3b)-2(3a-b) 24 3a-b 12 2a-3b 8 3 4 -3x-8 4 -9x-10+6x+2 4 (-9x-10)-2(-3x-1) 4 -3x-1 2 -9x-10 4 ④ + = = = ← 공약수 2로 약분한다. = & x+ y* ⑤ - - = = = = ⑥ + = = = = x ⑦ - = = = &- y+ * ⑧ - + = = = = &-a-1b* 2 -2a-b 2 -10a-5b 10 -8a-4b-2a-b 10 -2(4a+2b)+(-2a-b) 10 -2a-b 10 4a+2b 5 5 3 5 2 -15y+10 6 -9y+6-6y+4 6 3(-3y+2)-2(3y-2) 6 3y-2 3 -3y+2 2 5 6 10x 12 -2x-6y+12x+6y 12 2(-x-3y)+3(4x+2y) 12 4x+2y 4 -x-3y 6 2 3 6 9 -6a+15+6a-9 9 -3(2a-5)-(-6a+9) 9 -6a+9 9 2a-5 3 5 3 4 3 4x+5y 3 8x+10y 6 3x+9y+5x+y 6 3(x+3y)+(5x+y) 6 5x+y 6 x+3y 2 ↑ 공약수 5로 약분한다.

### �성취도테스트

( 1 )6a+2ab ( 2 )-(x-9)3 ( 3 ) -( 4 ) - - ( 5 ) ( 6 )-3a- b ( 7 ) + ( 8 )4a-a-2b 6 x yz xy z 1 3 5y x+4 3 c b 2 4 a x+y x-y

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4× +51 4 ( 9 )- (10)1 (11)- (12) -(13)14 (14)4 9 16 4 5 1 4 (15)-7 (16)- (17)9 (18)0 (19) (20)-17 9 2 3 1 2 <풀이> ( 9 )1-5a=1-5× =1- =-(10) = = = =1 (11) (-8a-6)= ×&-8× -6* = ×(-2-6) = ×(-8) =-4 5 1 10 1 10 1 4 1 10 1 10 6 6 1+5 6 6 4a+5 6 1 4 5 4 1 4 <풀이> (15)2a+3b=2×4+3×(-5)=8-15=-7 (16) = = =-(17)-a2+b2=-42+(-5)2=-16+25=9 (18)4x-6y=4×&- *-6×&- * =-2+2=0

(19)xy-x=&- *×&- *-&- * = + = + = = (20)4x+y2=4×&- *+&- *2 =-2+ =-17 9 1 9 1 3 1 2 2 3 4 6 3 6 1 6 1 2 1 6 1 2 1 3 1 2 1 3 1 2 1 2 2 4 -12+10 4 -3×4-2×(-5) 4 -3a-2b 4 (12)- + =- + =- + =- - =-(13)-x2-5x+10=-(-4)2-5×(-4)+10 =-16+20+10 =14 (14) + = + = + = + =4 16 4 0 7 4+12 4 -8+8 7 4-3×(-4) 4 2×(-4)+8 7 4-3x 4 2x+8 7 9 16 6 16 3 16 3 -8 3 16 3 2×(-4) 3 (-4)2 3 2x 3 x2 <풀이> ( 1 )a×6+2×b×a=6×a+2×a×b=6a+2ab ( 2 )(x-9)×(x-9)×(x-9)×(-1) =(-1)×(x-9)×(x-9)×(x-9) =-(x-9)3 ( 3 )-(x+y)÷(x-y)=-(x+y)× =-( 4 )4÷a+b÷(-2)+3÷(-c) =4× +b×&- *+3×&- * = - -( 5 )5÷(x+4)×y=5× ×y= ( 6 )a×(-3)-b÷3=(-3)×a-b× =-3a- b ( 7 )(x×y)÷z+x÷(y×z)=xy÷z+x÷yz =xy× +x× = + ( 8 )4×a-(a-2×b)÷6=4a-(a-2b)× =4a-a-2b 6 1 6 x yz xy z 1 yz 1 z 1 3 1 3 5y x+4 1 x+4 3 c b 2 4 a 1 c 1 2 1 a x+y x-y 1 x-y

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## K-4

### 정답및풀이

(21)- (22) (23)36 (24)-18 (25) 1 (26)0.8 20 11 12 1 12 <풀이> (21) - - = - -= + - =-(22) + + = + + =1- + = (23)(x+y-z)2 ={1+(-3)-4}2 =(-6)2 =36 (24)a-(b-c)=-5-{6-(-7)}=-5-13=-18 (25)a-(b-c)= -& - * = -& - * = - = (26)a-(b-c)=0.1-(-0.3-0.4)=0.1+0.7=0.8 1 20 1 20 2 20 4 20 5 20 2 20 1 5 1 4 1 10 11 12 3 12 4 12 1 4 1 -3 1 1 1 z 1 y 1 x 1 12 16 12 9 12 6 12 4 3 -3 4 1 2 z 3 y 4 x 2 (33)-4a+7b (34)5a-b+7 (35)-3y (36)-7x+5y+3z (37)7.5a2 -2.9ab+1.6b2 (38) -5x2 + x-8 3 3 5 <풀이> (33)(2a+3b)+(-6a+4b)=2a+3b-6a+4b =-4a+7b (34)(4a-5b+9)-(-a-4b+2) =4a-5b+9+a+4b-2 =5a-b+7 (35)(-3x-2y)+(5x+3y)-(2x+4y) =-3x-2y+5x+3y-2x-4y=-3y (36)(-5x+6z)-(2x-3y)+(2y-3z) =-5x+6z-2x+3y+2y-3z=-7x+5y+3z (37)(8a2-0.9ab)-(0.5a2+2ab-1.6b2) =8a2-0.9ab-0.5a2-2ab+1.6b2 =7.5a2 -2.9ab+1.6b2 (38)(-x2 +8x-3)-&- x+1*-&4x2 +8x- * =-x2+8x-3+ x-1-4x2-8x+ =-5x2+ x-8 3 3 5 4 3 3 5 4 3 3 5 (39)4a-5b-8c (40)-8x- y+ z (41)2a- b (42)-11x+15 (43)4a-3 (44)-15x-4 (45)3x+7y 1 2 9 5 1 3 (27)x (28)- a (29)6x-2y (30)- a+5b (31)-8x2-12x+7 (32)- ab-6xy 5 5 12 5 9 11 24 <풀이> (27)9x-6x-7x+5x=(9-6-7+5)x=x (28)- a+ a=- a+ a =&- + *a =- a (29)8x-5y+3y-2x=8x-2x-5y+3y=6x-2y (30)- a+5b-&- a*=- a+ a+5b =-5a+5b 9 7 9 12 9 7 9 4 3 11 24 9 24 20 24 9 24 20 24 3 8 5 6 (31)-17x2-8x-4+11-4x+9x2 = -17x2 +9x2 -8x-4x-4+11 =-8x2 -12x+7 (32) ab-xy- ab- xy = ab- ab-xy- xy =- ab-6xy 5 5 12 1 5 21 12 16 12 1 5 7 4 4 3

(37)

<풀이> (46) - = = = &x- *5 7 7x-5 7 3x-2+4x-3 7 (3x-2)-(-4x+3) 7 -4x+3 7 3x-2 7 (47) + = = = & a- * (48) - = = = &- y-1* (49)- + = = = a (50)- -= = = = & x-1y* 2 1 2 x-y 2 3x-3y 6 2x-4y+x+y 6 -2(-x+2y)-(-x-y) 6 -x-y 6 -x+2y 3 11 18 -3a+6b+14a-6b 18 -3(a-2b)+2(7a-3b) 18 7a-3b 9 a-2b 6 9 8 -9y-8 8 -3y+2-6y-10 8 (-3y+2)-2(3y+5) 8 3y+5 4 -3y+2 8 11 12 13 12 13a-11 12 4a-8+9a-3 12 4(a-2)+3(3a-1) 12 3a-1 4 a-2 3 (46) &x- * (47) & a- * (48) &- y-1* (49) a (50) & x-1y* 2 1 2 x-y 2 11 18 9 8 -9y-8 8 11 12 13 12 13a-11 12 5 7 7x-5 7 <풀이> (39) (40) (41)- (-8a+2b)=- ×(-8a)- ×2b =2a- b (42)-5x-3(2x-5)=-5x-6x+15=-11x+15 (43)5(2a-1)+2(-3a+1)=10a-5-6a+2 =4a-3 (44)8&- x+ *-6& +1*=-12x+2-3x-6 =-15x-4 (45)-2(x+2y)+4(-x-y)-3(-3x-5y) =-2x-4y-4x-4y+9x+15y =3x+7y x 2 1 4 3 2 1 2 1 4 1 4 1 4 � 9a-7b-2c +)≥-5a+2b -6c -6x+ 2y- z -} 2x+7y-2 z 3 1 5 -6x+ 2y- z +} -2x- y+ 2 z 7 3 1 5

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