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www.gitan.co.kr/ (02)586-1007(대)M - 61 ( 1 )
x
( 2 )b
( 3 )x
(y
+z
) ( 4 )x
, 5 ( 5 )a
(b
+3c
) ( 6 )x
(y
-1) ( 7 )a
(a
+2) ( 8 )-x
(x
+y
) ( 9 )5 (10)4 (11)3(3a
+2) (12)5(2b
-5) (13)2x
, 3y
(14)3(x
-3y
) (15)2(4x
+y
) (16)5(4a
-3b
) (17)4(4a
+5b
) (18)-2(3x
2+2y
) <풀이> ※ 다항식의 각 항에 공통인수가 있을 때에는 분 배법칙을 이용하여 공통인수로 묶어 내어 인수 분해한다.ma
+mb
=m
(a
+b
) ( 1 )ax
+ay
=a
×x
+a
×y
=a
(x
+y
) ( 2 )ab
-bc
=b
×a
-b
×c
=b
(a
-c
) ( 3 )xy
+xz
=x
×y
+x
×z
=x
(y
+z
) ( 4 )-cx
+5c
=(-c
)×x
-(-c
)×5=-c
(x
-5) <다른 풀이> -cx
+5c
=5c
-cx
=c
×5-c
×x
=c
(5-x
) ( 5 )ab
+3ac
=a
×b
+a
×3c
=a
(b
+3c
) ( 6 )xy
-x
=x
×y
-x
×1=x
(y
-1) ( 7 )a
2+2a
=a
×a
+a
×2=a
(a
+2) ( 8 )-x
2 -xy
=(-x
)×x
+(-x
)×y
=-x
(x
+y
) ( 9 )2x
+10=2×x
+2×5=2(x
+5) (10)4y
-28=4×y
-4×7=4(y
-7) (11)9a
+6=3×3a
+3×2=3(3a
+2) (12)10b
-25=5×2b
-5×5=5(2b
-5) (13)-8x
+12y
=(-4)×2x
-(-4)×3y
=-4(2x
-3y
) (14)3x
-9y
=3×x
-3×3y
=3(x
-3y
) (15)8x
+2y
=2×4x
+2×y
=2(4x
+y
) (16)20a
-15b
=5×4a
-5×3b
=5(4a
-3b
) (17)16a
+20b
=4×4a
+4×5b
=4(4a
+5b
) (18)-6x
2 -4y
=(-2)×3x
2 +(-2)×2y
=-2(3x
2 +2y
) M - 63 ( 1 )2ab
(x
+1) ( 2 )5xy
(a
-1) ( 3 )-4ax
(b
-2) ( 4 )2bx
(5a
-1) ( 5 )3xz
(2y
+3) ( 6 )3x
2(a
-b
) ( 7 )6y
2(x
+z
) ( 8 )-5xy
(x
+2) ( 9 )3xy
(3y
+x
) (10)2xz
(2y
2z
-3x
) (11)x
2(x
+1) (12)x
3(x
-y
) (13)-x
4(ax
-b
) (14)x
2y
2(x
-y
) (15)a
2b
2(3a
+4b
) (16)6ax
2(a
-1) (17)4xy
2 (y
2 +2) (18)-2axy
(y
+3x
) (19)5axy
2 (2x
2 +y
) (20)3x
2yz
2 (3x
-2z
) <풀이> ( 1 )2abx
+2ab
=2ab
×x
+2ab
×1=2ab
(x
+1) ( 2 )5axy
-5xy
=5xy
×a
-5xy
×1=5xy
(a
-1) ( 3 )-4abx
+8ax
=(-4ax
)×b
-(-4ax
)×2 =-4ax
(b
-2) M - 62 ( 1 )3x
( 2 )5x
(x
-4) ( 3 )a
, 1 ( 4 )2x
( 5 )4b
(2a
+3c
) ( 6 )4y
(x
-2) ( 7 )9x
(x
+y
) ( 8 )-6y
(x
+3y
)( 9 )3x
(5xy
+2) (10)2b
(5ab
-4)(11)ab
(x
+y
) (12)xy
(13)x
, 3 (14)by
(a
-x
) (15)ax
(x
+5) (16)xy
(y
-1) (17)xy
(x
+1) (18)-xy
(xy
+2) (19)xy
(4x
+y
) (20)ab
(a
2 -b
3) <풀이> ※ 분배법칙을 이용하여 전개한 식이므로 분배 법칙을 이용하여 괄호를 풀기 전의 식으로 고치 도록 한다. 또, 공통인수를 묶어 낼 때 공통인수 의 일부분만 묶어 내지 않도록 주의한다. ( 1 )9x
2 +3x
=3x
×3x
+3x
×1=3x
(3x
+1) ( 2 )5x
2-20x
=5x
×x
-5x
×4=5x
(x
-4) ( 3 )-7ax
+7x
=(-7x
)×a
-(-7x
)×1 =-7x
(a
-1) ( 4 )6xy
-8xz
=2x
×3y
-2x
×4z
=2x
(3y
-4z
) ( 5 )8ab
+12bc
=4b
×2a
+4b
×3c
=4b
(2a
+3c
) ( 6 )4xy
-8y
=4y
×x
-4y
×2=4y
(x
-2) ( 7 )9x
2 +9xy
=9x
×x
+9x
×y
=9x
(x
+y
) ( 8 )-6xy
-18y
2=(-6y
)×x
+(-6y
)×3y
=-6y
(x
+3y
) ( 9 )15x
2y
+6x
=3x
×5xy
+3x
×2=3x
(5xy
+2) (10)10ab
2 -8b
=2b
×5ab
-2b
×4=2b
(5ab
-4) (11)abx
+aby
=ab
×x
+ab
×y
=ab
(x
+y
) (12)axy
-bxy
=xy
×a
-xy
×b
=xy
(a
-b
) (13)-abx
+3ab
=(-ab
)×x
-(-ab
)×3 =-ab
(x
-3) (14)aby
-bxy
=by
×a
-by
×x
=by
(a
-x
) (15)ax
2+5ax
=ax
×x
+ax
×5=ax
(x
+5) (16)xy
2-xy
=xy
×y
-xy
×1=xy
(y
-1) (17)x
2y
+xy
=xy
×x
+xy
×1=xy
(x
+1) (18)-x
2y
2 -2xy
=(-xy
)×xy
+(-xy
)×2 =-xy
(xy
+2) (19)4x
2y
+xy
2 =xy
×4x
+xy
×y
=xy
(4x
+y
) (20)a
3b
-ab
4 =ab
×a
2-ab
×b
3=ab
(a
2 -b
3)( 4 )10
abx
-2bx
=2bx
×5a
-2bx
×1 =2bx
(5a
-1) ( 5 )6xyz
+9xz
=3xz
×2y
+3xz
×3=3xz
(2y
+3) ( 6 )3ax
2-3bx
2=3x
2×a
-3x
2×b
=3x
2(a
-b
) ( 7 )6xy
2 +6y
2z
=6y
2 ×x
+6y
2 ×z
=6y
2 (x
+z
) ( 8 )-5x
2y
-10xy
=(-5xy
)×x
+(-5xy
)×2 =-5xy
(x
+2) ( 9 )9xy
2+3x
2y
=3xy
×3y
+3xy
×x
=3xy
(3y
+x
) (10)4xy
2z
2 -6x
2z
=2xz
×2y
2z
-2xz
×3x
=2xz
(2y
2z
-3x
) (11)x
3+x
2=x
2×x
+x
2×1=x
2(x
+1) (12)x
4-x
3y
=x
3 ×x
-x
3 ×y
=x
3 (x
-y
) (13)-ax
5+bx
4=(-x
4 )×ax
-(-x
4 )×b
=-x
4(ax
-b
) (14)x
3y
2-x
2y
3=x
2y
2×x
-x
2y
2×y
=x
2y
2(x
-y
) (15)3a
3b
2+4a
2b
3=a
2b
2 ×3a
+a
2b
2 ×4b
=a
2b
2(3a
+4b
) (16)6a
2x
2-6ax
2=6ax
2 ×a
-6ax
2 ×1 =6ax
2(a
-1) (17)4xy
4+8xy
2=4xy
2 ×y
2+4xy
2 ×2 =4xy
2(y
2+2) (18)-2axy
2-6ax
2y
=(-2axy
)×y
+(-2axy
)×3x
=-2axy
(y
+3x
) (19)10ax
3y
2+5axy
3=5axy
2 ×2x
2+5axy
2 ×y
=5axy
2(2x
2+y
) (20)9x
3yz
2-6x
2yz
3=3x
2yz
2×3x
-3x
2yz
2×2z
=3x
2yz
2(3x
-2z
) M - 64 ( 1 )a
(x
+y
+z
) ( 2 )x
(a
+b
-c
) ( 3 )-a
(3x
+5y
-z
) ( 4 )2x
(2a
-3b
-c
) ( 5 )x
(x
+y
+z
) ( 6 )-ab
(x
2 -x
+c
) ( 7 )4x
(x
-y
+2) ( 8 )3x
(2x
-y
-3z
) ( 9 )x
(x
2+x
+1) (10)2x
(x
2+3x
-2) (11)-xy
(x
+y
-2) (12)5a
(x
2 -3y
2-2z
2) (13)xy
2(x
+2y
+z
) (14)-xyz
(x
-y
+z
) (15)3abc
(3ab
-2b
+4) (16)xy
2z
3(xy
2-3x
2z
-5yz
2) <풀이> ( 1 )ax
+ay
+az
=a
×x
+a
×y
+a
×z
=a
(x
+y
+z
) ( 2 )ax
+bx
-cx
=x
×a
+x
×b
-x
×c
=x
(a
+b
-c
) ( 3 )-3ax
-5ay
+az
=(-a
)×3x
+(-a
)×5y
-(-a
)×z
=-a
(3x
+5y
-z
) ( 4 )4ax
-6bx
-2cx
=2x
×2a
-2x
×3b
-2x
×c
=2x
(2a
-3b
-c
) ( 5 )x
2+xy
+xz
=x
×x
+x
×y
+x
×z
=x
(x
+y
+z
)( 6 )-
abx
2+abx
-abc
=(-ab
)×x
2-(-ab
)×x
+(-ab
)×c
=-ab
(x
2-x
+c
) ( 7 )4x
2-4xy
+8x
=4x
×x
-4x
×y
+4x
×2 =4x
(x
-y
+2) ( 8 )6x
2-3xy
-9xz
=3x
×2x
-3x
×y
-3x
×3z
=3x
(2x
-y
-3z
) ( 9 )x
3+x
2+x
=x
×x
2+x
×x
+x
×1=x
(x
2+x
+1) (10)2x
3+6x
2-4x
=2x
×x
2+2x
×3x
-2x
×2 =2x
(x
2+3x
-2) (11)-x
2y
-xy
2+2xy
=(-xy
)×x
+(-xy
)×y
-(-xy
)×2 =-xy
(x
+y
-2) (12)5ax
2-15ay
2-10az
2 =5a
×x
2-5a
×3y
2-5a
×2z
2 =5a
(x
2-3y
2-2z
2) (13)x
2y
2+2xy
3+xy
2z
=xy
2 ×x
+xy
2 ×2y
+xy
2 ×z
=xy
2(x
+2y
+z
) (14)-x
2yz
+xy
2z
-xyz
2=(-
xyz
)×x
-(-xyz
)×y
+(-xyz
)×z
=-xyz
(x
-y
+z
)(15)9
a
2b
2c
-6ab
2c
+12abc
=3
abc
×3ab
-3abc
×2b
+3abc
×4 =3abc
(3ab
-2b
+4) (16)x
2y
4z
3-3x
3y
2z
4-5xy
3z
5 =xy
2z
3 ×xy
2-xy
2z
3 ×3x
2z
-xy
2z
3 ×5yz
2 =xy
2z
3(xy
2-3x
2z
-5yz
2) M - 65 ( 1 )a
,b
( 2 )x
,a
( 3 )(x
+1)(a
-b
) ( 4 )(a
-4)(x
-y
) ( 5 ) (x
+y
)(a
+b
) ( 6 )(a
-b
)(x
+y
) ( 7 )(a
+3)(x
-1) ( 8 )(x
-5)(1-a
) ( 9 )2a
, 1 (10)(a
-b
)(1+3x
) (11)(x
+2)(2x
-3) (12)(2a
-5)(x
-y
) (13)(3x
+2)(a
+b
) (14)(3a
+5)(x
-2y
) (15)(4x
-1)(3a
+b
) (16)(x
-2y
)(3y
-5z
) (17)(2x
-3y
)(5a
+2b
) (18)(4a
+3b
)(4x
-3y
)<풀이> ※ (
a
+b
)x
+(a
+b
)y
를 인수분해할 때, 전개하지 말고 두 다항식 (a
+b
)x
와 (a
+b
)y
에 공통으로 들어 있는 인수a
+b
로 묶어 내면 다음과 같이 인수분해할 수 있다. (a
+b
)x
+(a
+b
)y
=(a
+b
)(x
+y
) ( 1 )x
(a
+b
)+2(a
+b
)=(a
+b
)(x
+2) ( 2 )x
(x
-y
)+a
(x
-y
)=(x
-y
)(x
+a
) ( 3 )a
(x
+1)-b
(x
+1)=(x
+1)(a
-b
) ( 4 )x
(a
-4)-y
(a
-4)=(a
-4)(x
-y
) ( 5 )(x
+y
)a
+(x
+y
)b
=(x
+y
)(a
+b
) ( 6 )(a
-b
)x
+(a
-b
)y
=(a
-b
)(x
+y
) ( 7 )x
(a
+3)-(a
+3)=(a
+3)(x
-1) ( 8 )(x
-5)-a
(x
-5)=(x
-5)(1-a
) ( 9 )2a
(x
+y
)+(x
+y
)=(x
+y
)(2a
+1) (10)(a
-b
)+3x
(a
-b
)=(a
-b
)(1+3x
) (11)2x
(x
+2)-3(x
+2)=(x
+2)(2x
-3) (12)(2a
-5)x
-(2a
-5)y
=(2a
-5)(x
-y
) (13)(3x
+2)a
+(3x
+2)b
=(3x
+2)(a
+b
) (14)x
(3a
+5)-2y
(3a
+5)=(3a
+5)(x
-2y
) (15)3a
(4x
-1)+b
(4x
-1)=(4x
-1)(3a
+b
) (16)3y
(x
-2y
)-5z
(x
-2y
)=(x
-2y
)(3y
-5z
) (17)5a
(2x
-3y
)+2b
(2x
-3y
)=(2x
-3y
)(5a
+2b
) (18)4x
(4a
+3b
)-3y
(4a
+3b
)=(4a
+3b
)(4x
-3y
) M - 66 ( 1 )a
,b
( 2 )4, 1 ( 3 )3(x
-y
)(x
-3) ( 4 )2(a
+b
)(x
+3y
) ( 5 ) 2(x
+y
)(3a
-4b
) ( 6 )3(a
-b
)(2a
+3b
) ( 7 )3b
,a
,c
( 8 )6x
(x
-y
)(a
+b
) ( 9 )x
(x
+4)(3x
-y
) (10)a
(x
-5)(5a
-1) (11)2x
(a
+b
)(4x
+1) (12)xy
(a
-1)(x
+y
) (13)2xy
(x
+y
)(2a
-3b
)(14)3x
2(x
-y
)(3a
-2b
) <풀이> ( 1 )5a
(x
-3)+5b
(x
-3)=(x
-3)(5a
+5b
) =5(x
-3)(a
+b
) ( 2 )4x
(a
+5)-4(a
+5)=(a
+5)(4x
-4) =4(a
+5)(x
-1) ( 3 )3x
(x
-y
)-9(x
-y
)=(x
-y
)(3x
-9) =3(x
-y
)(x
-3) ( 4 )2x
(a
+b
)+6y
(a
+b
)=(a
+b
)(2x
+6y
) =2(a
+b
)(x
+3y
) ( 5 )6a
(x
+y
)-8b
(x
+y
)=(x
+y
)(6a
-8b
) =2(x
+y
)(3a
-4b
) ( 6 )6a
(a
-b
)+9b
(a
-b
)=(a
-b
)(6a
+9b
) =3(a
-b
)(2a
+3b
) ( 7 )3ab
(x
+y
)+3bc
(x
+y
)=(x
+y
)(3ab
+3bc
) =3b
(x
+y
)(a
+c
) ( 8 )6ax
(x
-y
)+6bx
(x
-y
)=(x
-y
)(6ax
+6bx
) =6x
(x
-y
)(a
+b
) ( 9 )3x
2(x
+4)-xy
(x
+4)=(x
+4)(3x
2-xy
) =x
(x
+4)(3x
-y
) (10)5a
2(x
-5)-a
(x
-5)=(x
-5)(5a
2-a
) =a
(x
-5)(5a
-1) (11)8x
2(a
+b
)+2x
(a
+b
)=(a
+b
)(8x
2+2x
) =2x
(a
+b
)(4x
+1) (12)x
2y
(a
-1)+xy
2(a
-1)=(a
-1)(x
2y
+xy
2) =xy
(a
-1)(x
+y
) (13)4axy
(x
+y
)-6bxy
(x
+y
) =(x
+y
)(4axy
-6bxy
) =2xy
(x
+y
)(2a
-3b
) (14)9ax
2(x
-y
)-6bx
2(x
-y
) =(x
-y
)(9ax
2-6bx
2) =3x
2(x
-y
)(3a
-2b
) M - 67 ( 1 )x
(a
+b
) ( 2 )5(a
-b
) ( 3 )-4y
(x
-2z
) ( 4 )3x
(2x
-3y
) ( 5 )xy
(x
+y
) ( 6 )-ax
2(7a
+4) ( 7 )3a
2b
2(2b
+a
) ( 8 )2xyz
2(4xz
-3y
) ( 9 )x
(a
+b
+c
) (10)ab
(a
-b
+1) (11)4a
(2x
2 -y
2-3z
2) (12)(a
+b
)(x
+y
) (13)(2x
-y
)(1+5x
) (14)7(a
+3)(x
-1) (15)2x
(x
-4)(2x
-y
) (16)3x
2(x
-y
)(4a
+3b
) <풀이> ( 1 )ax
+bx
=x
×a
+x
×b
=x
(a
+b
) ( 2 )5a
-5b
=5×a
-5×b
=5(a
-b
) ( 3 )-4xy
+8yz
=(-4y
)×x
-(-4y
)×2z
=-4y
(x
-2z
) ( 4 )6x
2-9xy
=3x
×2x
-3x
×3y
=3x
(2x
-3y
) ( 5 )x
2y
+xy
2=xy
×x
+xy
×y
=xy
(x
+y
) ( 6 )-7a
2x
2-4ax
2=(-ax
2)×7a
+(-ax
2)×4 =-ax
2(7a
+4) ( 7 )6a
2b
3+3a
3b
2=3a
2b
2 ×2b
+3a
2b
2 ×a
=3a
2b
2(2b
+a
) ( 8 )8x
2yz
3-6xy
2z
2=2xyz
2 ×4xz
-2xyz
2 ×3y
=2xyz
2(4xz
-3y
) ( 9 )ax
+bx
+cx
=x
×a
+x
×b
+x
×c
=x
(a
+b
+c
)M - 68 ( 1 )
x
, 1 ( 2 )3, 3, 3 ( 3 )(x
+5)2 ( 4 )(x
-2)2 ( 5 ) (x
+4)2 ( 6 )(x
-6)2 ( 7 )(x
+7)2 ( 8 )(x
-8)2 ( 9 )(x
+9)2 (10)(x
-1)2 (11)(x
+3)2 (12)(x
-4)2 (13)(x
+6)2 (14)(x
-5)2 <풀이> ※ 주어진 식을a
2+2ab
+b
2,a
2-2ab
+b
2의 꼴 로 고친다. ( 1 )x
2+2x
+1=x
2+2×x
×1+12=(x
+1)2 ( 2 )x
2-6x
+9=x
2-2×x
×3+32=(x
-3)2 ( 3 )x
2+10x
+25=x
2+2×x
×5+52=(x
+5)2 ( 4 )x
2-4x
+4=x
2-2×x
×2+22=(x
-2)2 ( 5 )x
2+8x
+16=x
2+2×x
×4+42=(x
+4)2 ( 6 )x
2-12x
+36=x
2-2×x
×6+62=(x
-6)2 ( 7 )x
2+14x
+49=x
2+2×x
×7+72=(x
+7)2 ( 8 )x
2-16x
+64=x
2-2×x
×8+82=(x
-8)2 ( 9 )x
2+18x
+81=x
2+2×x
×9+92=(x
+9)2 (10)x
2-2x
+1=x
2-2×x
×1+12=(x
-1)2 (11)x
2+6x
+9=x
2+2×x
×3+32=(x
+3)2 (12)x
2-8x
+16=x
2-2×x
×4+42=(x
-4)2 (13)x
2+12x
+36=x
2+2×x
×6+62=(x
+6)2 (14)x
2-10x
+25=x
2-2×x
×5+52=(x
-5)2 ●2+2×●×▲+▲2 (● + ▲)2 � � ●2-2×●×▲+▲2 (● - ▲)2 � � M - 69 ( 1 )2x
, 1 ( 2 )2, 2, 2 ( 3 )(2x
+5)2 ( 4 )(3x
-5)2 ( 5 ) (3x
+1)2 ( 6 )(2x
-3)2 ( 7 )(3x
+4)2 ( 8 )(2x
-7)2 ( 9 )(2x
+9)2 (10)(3x
-7)2 (11)(4x
+3)2 (12)(6x
-5)2 (13)(3x
+8)2 (14)(5x
-4)2 (15)(7x
+2)2 (16)(3x
-10)2 <풀이> ( 1 )4x
2+4x
+1=(2x
)2+2×2x
×1+12=(2x
+1)2 ( 2 )9x
2-12x
+4=(3x
)2 -2×3x
×2+22=(3x
-2)2 ( 3 )4x
2+20x
+25=(2x
)2+2×2x
×5+52 =(2x
+5)2 ( 4 )9x
2-30x
+25=(3x
)2-2×3x
×5+52 =(3x
-5)2 ( 5 )9x
2+6x
+1=(3x
)2+2×3x
×1+12=(3x
+1)2 ( 6 )4x
2-12x
+9=(2x
)2-2×2x
×3+32=(2x
-3)2 ( 7 )9x
2+24x
+16=(3x
)2+2×3x
×4+42 =(3x
+4)2 ( 8 )4x
2-28x
+49=(2x
)2-2×2x
×7+72 =(2x
-7)2 ( 9 )4x
2+36x
+81=(2x
)2+2×2x
×9+92 =(2x
+9)2 (10)9x
2-42x
+49=(3x
)2-2×3x
×7+72 =(3x
-7)2 (11)16x
2+24x
+9=(4x
)2+2×4x
×3+32 =(4x
+3)2 (12)36x
2-60x
+25=(6x
)2-2×6x
×5+52 =(6x
-5)2 (13)9x
2+48x
+64=(3x
)2+2×3x
×8+82 =(3x
+8)2 (14)25x
2-40x
+16=(5x
)2-2×5x
×4+42 =(5x
-4)2 (15)49x
2+28x
+4=(7x
)2+2×7x
×2+22 =(7x
+2)2 (16)9x
2-60x
+100=(3x
)2-2×3x
×10+102 =(3x
-10)2 M - 70 ( 1 )(x
+y
)2 ( 2 )x
,y
( 3 )4y
, 4y
, 4y
( 4 )(x
-7y
)2 ( 5 ) (x
+2y
)2 ( 6 )(x
-3y
)2 ( 7 )(x
+5y
)2 ( 8 )(x
-9y
)2 ( 9 )(x
+3y
)2 (10)(x
-2y
)2 (11)(x
+6y
)2 (12)(x
-5y
)2 (13)(x
+7y
)2 (14)(x
-4y
)2 (15)(x
+9y
)2 (16)(x
-8y
)2 (10)a
2b
-ab
2+ab
=ab
×a
-ab
×b
+ab
×1 =ab
(a
-b
+1) (11)8ax
2-4ay
2-12az
2 =4a
×2x
2-4a
×y
2-4a
×3z
2 =4a
(2x
2-y
2-3z
2) (12)(a
+b
)x
+(a
+b
)y
=(a
+b
)(x
+y
) (13)(2x
-y
)+5x
(2x
-y
)=(2x
-y
)(1+5x
) (14)7x
(a
+3)-7(a
+3) =(a
+3)(7x
-7) =7(a
+3)(x
-1) (15)4x
2(x
-4)-2xy
(x
-4) =(x
-4)(4x
2 -2xy
) =2x
(x
-4)(2x
-y
) (16)12ax
2(x
-y
)+9bx
2(x
-y
) =(x
-y
)(12ax
2+9bx
2) =3x
2(x
-y
)(4a
+3b
)<풀이> ( 1 )
x
2+2xy
+y
2=x
2+2×x
×y
+y
2=(x
+y
)2 ( 2 )x
2-2xy
+y
2=x
2-2×x
×y
+y
2=(x
-y
)2 ( 3 )x
2+8xy
+16y
2=x
2+2×x
×4y
+(4y
)2 =(x
+4y
)2 ( 4 )x
2-14xy
+49y
2=x
2-2×x
×7y
+(7y
)2 =(x
-7y
)2 ( 5 )x
2+4xy
+4y
2=x
2+2×x
×2y
+(2y
)2 =(x
+2y
)2 ( 6 )x
2-6xy
+9y
2=x
2-2×x
×3y
+(3y
)2 =(x
-3y
)2 ( 7 )x
2+10xy
+25y
2=x
2+2×x
×5y
+(5y
)2 =(x
+5y
)2 ( 8 )x
2-18xy
+81y
2=x
2-2×x
×9y
+(9y
)2 =(x
-9y
)2 ( 9 )x
2+6xy
+9y
2=x
2+2×x
×3y
+(3y
)2 =(x
+3y
)2 (10)x
2-4xy
+4y
2=x
2-2×x
×2y
+(2y
)2 =(x
-2y
)2 (11)x
2+12xy
+36y
2=x
2+2×x
×6y
+(6y
)2 =(x
+6y
)2 (12)x
2-10xy
+25y
2=x
2-2×x
×5y
+(5y
)2 =(x
-5y
)2 (13)x
2+14xy
+49y
2=x
2+2×x
×7y
+(7y
)2 =(x
+7y
)2 (14)x
2-8xy
+16y
2=x
2-2×x
×4y
+(4y
)2 =(x
-4y
)2 (15)x
2+18xy
+81y
2=x
2+2×x
×9y
+(9y
)2 =(x
+9y
)2 (16)x
2-16xy
+64y
2=x
2-2×x
×8y
+(8y
)2 =(x
-8y
)2 M - 71 ( 1 )2x
, 2x
, 2x
( 2 )(3x
-4y
)2 ( 3 )(2x
+5y
)2 ( 4 )7y
, 7y
, 7y
( 5 ) (3x
+2y
)2 ( 6 )(2x
-7y
)2 ( 7 )(3x
+5y
)2 ( 8 )(2x
-9y
)2 ( 9 )(2x
+3y
)2 (10)(3x
-y
)2 (11)(4x
+7y
)2 (12)(5x
-8y
)2 (13)(3x
+8y
)2 (14)(7x
-5y
)2 (15)(3x
+10y
)2 (16)(6x
-7y
)2 <풀이> ( 1 )4x
2+4xy
+y
2=(2x
)2+2×2x
×y
+y
2 =(2x
+y
)2 ( 2 )9x
2-24xy
+16y
2=(3x
)2 -2×3x
×4y
+(4y
)2 =(3x
-4y
)2 ( 3 )4x
2+20xy
+25y
2=(2x
)2+2×2x
×5y
+(5y
)2 =(2x
+5y
)2 ( 4 )9x
2-42xy
+49y
2=(3x
)2-2×3x
×7y
+(7y
)2 =(3x
-7y
)2 ( 5 )9x
2+12xy
+4y
2=(3x
)2+2×3x
×2y
+(2y
)2 =(3x
+2y
)2 ( 6 )4x
2-28xy
+49y
2=(2x
)2-2×2x
×7y
+(7y
)2 =(2x
-7y
)2 ( 7 )9x
2+30xy
+25y
2=(3x
)2+2×3x
×5y
+(5y
)2 =(3x
+5y
)2 ( 8 )4x
2-36xy
+81y
2=(2x
)2-2×2x
×9y
+(9y
)2 =(2x
-9y
)2 ( 9 )4x
2+12xy
+9y
2=(2x
)2+2×2x
×3y
+(3y
)2 =(2x
+3y
)2 (10)9x
2-6xy
+y
2=(3x
)2-2×3x
×y
+y
2 =(3x
-y
)2 (11)16x
2+56xy
+49y
2=(4x
)2+2×4x
×7y
+(7y
)2 =(4x
+7y
)2 (12)25x
2-80xy
+64y
2=(5x
)2-2×5x
×8y
+(8y
)2 =(5x
-8y
)2 (13)9x
2+48xy
+64y
2=(3x
)2+2×3x
×8y
+(8y
)2 =(3x
+8y
)2 (14)49x
2-70xy
+25y
2=(7x
)2-2×7x
×5y
+(5y
)2 =(7x
-5y
)2 (15)9x
2+60xy
+100y
2 =(3x
)2+2×3x
×10y
+(10y
)2 =(3x
+10y
)2 (16)36x
2-84xy
+49y
2=(6x
)2 -2×6x
×7y
+(7y
)2 =(6x
-7y
)2 M - 72 ( 1 )xy
, 2,xy
( 2 )(ax
-3)2 ( 3 )(2xy
+5)2 ( 4 )(3ab
-7x
)2 ( 5 ) , , ( 6 )&x
- *2( 7 )&
x
+ *2 ( 8 )&x
- *2 ( 9 )&2x
+ *2(10)&3
x
- *2 (11)&2x
+ *2 (12)&3x
- *2(13)&3
x
+y
*2 (14)&2x
-y
*2 (15)&3x
+y
*2(16)&4
x
-34y
*2 2 3 1 4 1 2 2 3 3 4 1 3 1 2 3 4 2 3 1 3 1 2 1 2 1 2 <풀이> ( 1 )x
2y
2+4xy
+4=(xy
)2+2×xy
×2+22 =(xy
+2)2( 2 )
a
2x
2-6ax
+9=(ax
)2-2×ax
×3+32 =(ax
-3)2 ( 3 )4x
2y
2+20xy
+25=(2xy
)2+2×2xy
×5+52 =(2xy
+5)2 ( 4 )9a
2b
2-42abx
+49x
2 =(3ab
)2-2×3ab
×7x
+(7x
)2 =(3ab
-7x
)2 ( 5 )x
2+x
+ =x
2+2×x
× +& * 2 ( 5 )x
2+x
+ =&x
+ *2 ( 6 )x
2-x
+ =x
2-2×x
× +& * 2 ( 5 )x
2-x
+ =&x
- *2 ( 7 )x
2+x
+ =x
2+2×x
× +& * 2 ( 7 )x
2+x
+ =&x
+ *2 ( 8 )x
2-x
+ =x
2-2×x
× +& * 2 ( 7 )x
2+x
+ =&x
- *2 ( 9 )4x
2+2x
+ =(2x
)2 +2×2x
× +& * 2 ( 9 )4x
2+2x
+ =&2x
+ *2 (10)9x
2-2x
+ =(3x
)2-2×3x
× +& * 2 ( 9 )4x
2+2x
+ =&3x
- *2 (11)4x
2+3x
+ =(2x
)2 +2×2x
× +& * 2 ( 9 )4x
2+2x
+ = &2x
+ *2 (12)9x
2-4x
+ =(3x
)2-2×3x
× +& * 2 ( 9 )4x
2+2x
+ =&3x
- *2 (13)9x
2+3xy
+y
2=(3x
)2+2×3x
×y
+&y
*2 ( 9 )4x
2+2xy
+y
2=&3x
+y
*2 (14)4x
2-xy
+y
2=(2x
)2-2×2x
×y
+&y
*2 ( 9 )4x
2+xy
+y
2=&2x
-1y
*2 4 1 4 1 4 1 4 1 16 1 2 1 4 1 2 1 2 1 4 2 3 1 4 2 3 2 3 4 9 3 4 1 4 3 4 3 4 9 16 1 3 1 4 1 3 1 3 1 9 1 2 1 4 1 2 1 2 1 4 3 4 1 4 3 4 3 4 9 16 3 2 2 3 1 4 1 4 2 3 2 3 4 9 4 3 1 3 1 3 1 3 1 9 2 3 1 2 1 4 1 2 1 2 1 4 (15)9x
2+4xy
+y
2=(3x
)2+2×3x
×y
+&y
*2 ( 9 )4x
2+2xy
+y
2=&3x
+y
*2 (16)16x
2-6xy
+y
2 ( 9 )=(4x
)2 -2×4x
×y
+&y
*2 ( 9 )=&4x
-34y
*2 3 4 3 4 9 16 2 3 1 4 2 3 2 3 4 9 M - 73 ( 1 )5, 5, 1 ( 2 )2(x
-3)2 ( 3 )3(3x
+2)2 ( 4 )4, 4, 2y
( 5 ) 3(x
+3y
)2 ( 6 )5(2x
-3y
)2 ( 7 )x
(x
+4)2 ( 8 )2x
(3x
-1)2 ( 9 )3x
(a
+3b
)2 (10)2a
(2xy
-3)2 (11) 3ab
(3x
+2y
)2 (12)-(x
-y
)2 (13)-(2x
+5y
)2 (14)-(x
2+y
2)2 <풀이> ( 1 )5x
2+10x
+5=5(x
2+2x
+1)
=5(x
2+2×x
×1+12) =5(x
+1)2 ( 2 )2x
2-12x
+18=2(x
2 -6x
+9) =2(x
2-2×x
×3+32) =2(x
-3)2 ( 3 )27x
2+36x
+12=3(9x
2+12x
+4) =3{(3x
)2 +2×3x
×2+22} =3(3x
+2)2 ( 4 )4x
2-16xy
+16y
2=4(x
2-4xy
+4y
2) =4{x
2-2×x
×2y
+(2y
)2} =4(x
-2y
)2 ( 5 )3x
2+18xy
+27y
2=3(x
2+6xy
+9y
2) =3{x
2+2×x
×3y
+(3y
)2} =3(x
+3y
)2 ( 6 )20x
2-60xy
+45y
2 =5(4x
2-12xy
+9y
2) =5{(2x
)2-2×2x
×3y
+(3y
)2} =5(2x
-3y
)2 ( 7 )x
3+8x
2+16x
=x
(x
2 +8x
+16) =x
(x
2+2×x
×4+42) =x
(x
+4)2 ( 8 )18x
3-12x
2+2x
=2x
(9x
2-6x
+1) =2x
{(3x
)2 -2×3x
×1+12} =2x
(3x
-1)2( 9 )3
a
2x
+18abx
+27b
2x
=3x
(a
2+6ab
+9b
2) =3x
{a
2+2×a
×3b
+(3b
)2} =3x
(a
+3b
)2 (10)8ax
2y
2-24axy
+18a
=2a
(4x
2y
2-12xy
+9) =2a
{(2xy
)2-2×2xy
×3+32} =2a
(2xy
-3)2(11)27
abx
2+36abxy
+12aby
2=3
ab
(9x
2+12xy
+4y
2) =3ab
{(3x
)2+2×3x
×2y
+(2y
)2} =3ab
(3x
+2y
)2 (12)-x
2+2xy
-y
2=-(x
2-2xy
+y
2) =-(x
2-2×x
×y
+y
2) =-(x
-y
)2 (13)-4x
2-20xy
-25y
2 =-(4x
2+20xy
+25y
2) =-{(2x
)2+2×2x
×5y
+(5y
)2} =-(2x
+5y
)2 (14)-x
4-2x
2y
2-y
4=-(x
4 +2x
2y
2+y
4) =-{(x
2)2+2×x
2 ×y
2+(y
2)2} =-(x
2+y
2)2 M - 74 ( 1 )(x
+2)2 ( 2 )(x
-7)2 ( 3 )(x
+8)2 ( 4 )(2x
-5)2 ( 5 ) (3x
+7)2 ( 6 )(5x
-4)2 ( 7 )(x
+6y
)2 ( 8 )(x
-9y
)2 ( 9 )(3x
+4y
)2 (10)(4x
-5y
)2 (11)(xy
+3)2 (12) &x
- *2 (13)&2x
+ *2 (14)5(x
-2)2 (15)3(x
+4y
)2 (16)-x
(x
-5)2 3 2 1 2 <풀이> ( 1 )x
2+4x
+4=x
2+2×x
×2+22=(x
+2)2 ( 2 )x
2-14x
+49=x
2-2×x
×7+72=(x
-7)2 ( 3 )x
2+16x
+64=x
2+2×x
×8+82=(x
+8)2 ( 4 )4x
2-20x
+25=(2x
)2-2×2x
×5+52 =(2x
-5)2 ( 5 )9x
2+42x
+49=(3x
)2 +2×3x
×7+72 =(3x
+7)2 ( 6 )25x
2-40x
+16=(5x
)2-2×5x
×4+42 =(5x
-4)2 ( 7 )x
2+12xy
+36y
2=x
2+2×x
×6y
+(6y
)2 =(x
+6y
)2 ( 8 )x
2-18xy
+81y
2=x
2-2×x
×9y
+(9y
)2 =(x
-9y
)2 ( 9 )9x
2+24xy
+16y
2=(3x
)2+2×3x
×4y
+(4y
)2 =(3x
+4y
)2 (10)16x
2-40xy
+25y
2=(4x
)2-2×4x
×5y
+(5y
)2 =(4x
-5y
)2 (11)x
2y
2+6xy
+9=(xy
)2+2×xy
×3+32=(xy
+3)2 (12)x
2-x
+ =x
2-2×x
× +& * 2 =&x
- *2 (13)4x
2+6x
+ =(2x
)2+2×2x
× +& * 2 (13)4x
2+6x
+ =&2x
+ *2 (14)5x
2-20x
+20=5(x
2-4x
+4) =5(x
2-2×x
×2+22) =5(x
-2)2 (15)3x
2+24xy
+48y
2=3(x
2 +8xy
+16y
2) =3{x
2+2×x
×4y
+(4y
)2} =3(x
+4y
)2 (16)-x
3+10x
2-25x
=-x
(x
2-10x
+25) =-x
(x
2 -2×x
×5+52) =-x
(x
-5)2 3 2 9 4 3 2 3 2 9 4 1 2 1 2 1 2 1 4 M - 75 ( 1 )y
(x
+z
) ( 2 )4(2a
-3b
) ( 3 )ab
(x
+5) ( 4 )3xz
(3xy
-2z
) ( 5 ) 3x
(x
+y
+3) ( 6 )2abc
(4a
-3b
+5) ( 7 )(x
-6)(1+a
) ( 8 )5x
(a
+2)(x
-2) ( 9 )(x
+4)2 (10)(2x
-7)2 (11)(3x
+5)2 (12)(x
-8y
)2 (13)(4x
+9y
)2 (14)&3x
- *2 (15)3(2x
-3)2 (16) 2a
(x
+4y
)2 4 3 <풀이> ( 1 )xy
+yz
=y
×x
+y
×z
=y
(x
+z
) ( 2 )8a
-12b
=4×2a
-4×3b
=4(2a
-3b
) ( 3 )abx
+5ab
=ab
×x
+ab
×5=ab
(x
+5) ( 4 )9x
2yz
-6xz
2=3xz
×3xy
-3xz
×2z
=3xz
(3xy
-2z
) ( 5 )3x
2+3xy
+9x
=3x
×x
+3x
×y
+3x
×3 =3x
(x
+y
+3) ( 6 )8a
2bc
-6ab
2c
+10abc
=2
abc
×4a
-2abc
×3b
+2abc
×5 =2abc
(4a
-3b
+5)( 7 )(
x
-6)+a
(x
-6)=(x
-6)(1+a
)( 8 )5
x
2(a
+2)-10x
(a
+2)=(a
+2)(5x
2-10x
)( 9 )
x
2+8x
+16=x
2+2×x
×4+42=(x
+4)2 (10)4x
2-28x
+49=(2x
)2-2×2x
×7+72=(2x
-7)2 (11)9x
2+30x
+25=(3x
)2+2×3x
×5+52 =(3x
+5)2 (12)x
2-16xy
+64y
2=x
2-2×x
×8y
+(8y
)2 =(x
-8y
)2 (13)16x
2+72xy
+81y
2=(4x
)2+2×4x
×9y
+(9y
)2 =(4x
+9y
)2 (14)9x
2-8x
+ =(3x
)2-2×3x
× +& * 2 (13)4x
2+6x
+ =&3x
- *2 (15)12x
2-36x
+27=3(4x
2-12x
+9) =3{(2x
)2 -2×2x
×3+32} =3(2x
-3)2 (16)2ax
2+16axy
+32ay
2 =2a
(x
2+8xy
+16y
2) =2a
{x
2 +2×x
×4y
+(4y
)2} =2a
(x
+4y
)2 4 3 9 4 4 3 4 3 16 9 M - 76 ( 1 )1, 1 ( 2 )(x
+2)(x
-2) ( 3 )(x
+3)(x
-3) ( 4 )(x
+4)(x
-4) ( 5 ) 6, 6, 6 ( 6 )(x
+7)(x
-7) ( 7 )(x
+8)(x
-8) ( 8 )(x
+9)(x
-9) ( 9 )2, 2 (10)(3+x
)(3-x
) (11)(6+x
)(6-x
) (12)(8+x
)(8-x
) (13)(9+x
)(9-x
) (14)1, 1, 1 (15)(4+x
)(4-x
) (16)(5+x
)(5-x
) (17)(7+x
)(7-x
) (18)(10+x
)(10-x
) <풀이> ( 1 )x
2-1=x
2-12=(x
+1)(x
-1) ( 2 )x
2-4=x
2-22=(x
+2)(x
-2) ( 3 )x
2-9=x
2-32=(x
+3)(x
-3) ( 4 )x
2-16=x
2-42=(x
+4)(x
-4) ( 5 )x
2-36=x
2-62=(x
+6)(x
-6) ( 6 )x
2-49=x
2-72=(x
+7)(x
-7) ( 7 )x
2-64=x
2-82=(x
+8)(x
-8) ( 8 )x
2-81=x
2-92=(x
+9)(x
-9) ( 9 )4-x
2=22-x
2=(2+x
)(2-x
) (10)9-x
2=32-x
2=(3+x
)(3-x
) (11)36-x
2=62-x
2=(6+x
)(6-x
) (12)64-x
2=82-x
2=(8+x
)(8-x
) (13)81-x
2=92-x
2=(9+x
)(9-x
) (14)-x
2+1=1-x
2=12-x
2=(1+x
)(1-x
) <다른 풀이> -x
2+1=-(x
2-1)=-(x
2-12)=-(x
+1)(x
-1) (15)-x
2+16=16-x
2=42-x
2=(4+x
)(4-x
) (16)-x
2+25=25-x
2=52-x
2=(5+x
)(5-x
) (17)-x
2+49=49-x
2=72-x
2=(7+x
)(7-x
) (18)-x
2+100=100-x
2=102-x
2=(10+x
)(10-x
) M - 77 ( 1 )(x
+y
)(x
-y
) ( 2 )4y
, 4y
( 3 )(x
+5y
)(x
-5y
) ( 4 )(x
+8y
)(x
-8y
) ( 5 ) (x
+9y
)(x
-9y
) ( 6 )(x
+2y
)(x
-2y
) ( 7 )(x
+3y
)(x
-3y
) ( 8 )(x
+6y
)(x
-6y
) ( 9 )(x
+7y
)(x
-7y
) (10)(x
+10y
)(x
-10y
) (11) , , (12)&x
+ *&x
- *(13)& +
x
*& -x
* (14)& +x
*& -x
* (15)&x
+y
*&x
-y
* (16)&x
+y
*&x
-y
*(17)& +
x
*& -x
* (18)& +x
*& -x
* (19)(xy
+9)(xy
-9) (20)(8+xy
)(8-xy
) 3 4 3 4 2 3 2 3 1 6 1 6 1 3 1 3 1 7 1 7 1 5 1 5 1 4 1 4 1 2 1 2 1 2 <풀이> ( 1 )x
2-y
2=(x
+y
)(x
-y
) ( 2 )x
2-16y
2=x
2-(4y
)2=(x
+4y
)(x
-4y
) ( 3 )x
2-25y
2=x
2-(5y
)2=(x
+5y
)(x
-5y
) ( 4 )x
2-64y
2=x
2-(8y
)2=(x
+8y
)(x
-8y
) ( 5 )x
2-81y
2=x
2-(9y
)2=(x
+9y
)(x
-9y
) ( 6 )x
2-4y
2=x
2-(2y
)2=(x
+2y
)(x
-2y
) ( 7 )x
2-9y
2=x
2-(3y
)2=(x
+3y
)(x
-3y
) ( 8 )x
2-36y
2=x
2-(6y
)2=(x
+6y
)(x
-6y
) ( 9 )x
2-49y
2=x
2-(7y
)2=(x
+7y
)(x
-7y
) (10)x
2-100y
2=x
2-(10y
)2=(x
+10y
)(x
-10y
)(11)
x
2- =x
2-& *2=&x
+ *&x
- *(12)
x
2- =x
2-& *2=&x
+ *&x
- *(13) -
x
2=& *2-x
2=& +x
*& -x
*(14) -
x
2=& *2-x
2=& +x
*& -x
*(15)
x
2-y
2=x
2-&
y
*2=&x
+y
*&x
-y
*(16)
x
2-y
2=x
2-&y
*2=&x
+y
*&x
-1y
*6 1 6 1 6 1 36 1 3 1 3 1 3 1 9 1 7 1 7 1 7 1 49 1 5 1 5 1 5 1 25 1 4 1 4 1 4 1 16 1 2 1 2 1 2 1 4
(17)-
x
2+ = -x
2=& *2-x
2=& +x
*& -x
* (18)-x
2+ = -x
2=& *2-x
2 (18)-x
2+ = -x
2=& +x
*& -x
* (19)x
2y
2-81=(xy
)2-92=(xy
+9)(xy
-9) (20)64-x
2y
2=82-(xy
)2=(8+xy
)(8-xy
) 3 4 3 4 9 16 9 16 3 4 9 16 9 16 2 3 2 3 2 3 4 9 4 9 M - 78 ( 1 )2x
, 2x
( 2 )(3x
+2)(3x
-2) ( 3 )(2x
+5)(2x
-5) ( 4 )(3x
+7)(3x
-7) ( 5 ) (2x
+9)(2x
-9) ( 6 )(3x
+8)(3x
-8) ( 7 )(6x
+1)(6x
-1) ( 8 )(4x
+3)(4x
-3) ( 9 )(5x
+6)(5x
-6) (10)(7x
+4)(7x
-4) (11)(3+2x
)(3-2x
) (12)(1+3x
)(1-3x
) (13)(6+2x
)(6-2x
) (14)3x
, 3x
, 3x
(15)(7+2x
)(7-2x
) (16)(2+3x
)(2-3x
) (17)(3+4x
)(3-4x
) (18)(8+5x
)(8-5x
) (19)(4+9x
)(4-9x
) (20)(9+8x
)(9-8x
) <풀이> ( 1 )4x
2-1=(2x
)2-12=(2x
+1)(2x
-1) ( 2 )9x
2-4=(3x
)2 -22=(3x
+2)(3x
-2) ( 3 )4x
2-25=(2x
)2 -52=(2x
+5)(2x
-5) ( 4 )9x
2-49=(3x
)2-72=(3x
+7)(3x
-7) ( 5 )4x
2-81=(2x
)2-92=(2x
+9)(2x
-9) ( 6 )9x
2-64=(3x
)2 -82=(3x
+8)(3x
-8) ( 7 )36x
2-1=(6x
)2 -12=(6x
+1)(6x
-1) ( 8 )16x
2-9=(4x
)2-32=(4x
+3)(4x
-3) ( 9 )25x
2-36=(5x
)2-62=(5x
+6)(5x
-6) (10)49x
2-16=(7x
)2 -42=(7x
+4)(7x
-4) (11)9-4x
2=32-(2x
)2=(3+2x
)(3-2x
) (12)1-9x
2=12-(3x
)2=(1+3x
)(1-3x
) (13)36-4x
2=62-(2x
)2=(6+2x
)(6-2x
) (14)25-9x
2=52-(3x
)2=(5+3x
)(5-3x
) (15)49-4x
2=72-(2x
)2=(7+2x
)(7-2x
) (16)-9x
2+4=4-9x
2=22-(3x
)2=(2+3x
)(2-3x
) (17)-16x
2+9=9-16x
2=32-(4x
)2 =(3+4x
)(3-4x
) (18)-25x
2+64=64-25x
2=82-(5x
)2 =(8+5x
)(8-5x
) (19)-81x
2+16=16-81x
2=42-(9x
)2 =(4+9x
)(4-9x
) (20)-64x
2+81=81-64x
2=92-(8x
)2 =(9+8x
)(9-8x
) M - 79 ( 1 )(2x
+y
)(2x
-y
) ( 2 )(3x
+4y
)(3x
-4y
) ( 3 )(2x
+7y
)(2x
-7y
) ( 4 )(3x
+8y
)(3x
-8y
) ( 5 ) (2x
+9y
)(2x
-9y
) ( 6 )(3x
+2y
)(3x
-2y
) ( 7 )(4x
+5y
)(4x
-5y
) ( 8 )(8x
+y
)(8x
-y
) ( 9 )(7x
+3y
)(7x
-3y
) (10)(5x
+6y
)(5x
-6y
)(11)&2
x
+ *&2x
- * (12)&3x
+ *&3x
- *(13)&5+
x
*&5-x
* (14)&4+x
*&4-x
* (15)&2x
+y
*&2x
-y
*(16)&3x
+y
*&3x
-y
*(17)& +4
x
*& -4x
* (18)& +x
*& -x
* (19)(5xy
+7)(5xy
-7) (20)(9+6xy
)(9-6xy
) 1 3 1 2 1 3 1 2 2 3 2 3 3 4 3 4 2 3 2 3 1 5 1 5 1 4 1 4 1 2 1 2 1 3 1 3 <풀이> ( 1 )4x
2-y
2=(2x
)2 -y
2=(2x
+y
)(2x
-y
) ( 2 )9x
2-16y
2=(3x
)2-(4y
)2=(3x
+4y
)(3x
-4y
) ( 3 )4x
2-49y
2=(2x
)2-(7y
)2=(2x
+7y
)(2x
-7y
) ( 4 )9x
2-64y
2=(3x
)2-(8y
)2=(3x
+8y
)(3x
-8y
) ( 5 )4x
2-81y
2=(2x
)2-(9y
)2=(2x
+9y
)(2x
-9y
) ( 6 )9x
2-4y
2=(3x
)2-(2y
)2=(3x
+2y
)(3x
-2y
) ( 7 )16x
2-25y
2=(4x
)2-(5y
)2=(4x
+5y
)(4x
-5y
) ( 8 )64x
2-y
2=(8x
)2 -y
2=(8x
+y
)(8x
-y
) ( 9 )49x
2-9y
2=(7x
)2-(3y
)2=(7x
+3y
)(7x
-3y
) (10)25x
2-36y
2=(5x
)2-(6y
)2=(5x
+6y
)(5x
-6y
)(11)4
x
2- =(2x
)2-& *2=&2x
+ *&2x
- *(12)9
x
2- =(3x
)2-& *2=&3
x
+ *&3x
- *(13)25-
x
2=52-&x
*2 (13)25-x
2=&5+x
*&5-x
* (14)16-x
2=42-&x
*2 (14)16-x
2=&4+x
*&4-x
* (15)4x
2-y
2=(2x
)2-&y
*2 (15)4x
2-y
2=&2x
+y
*&2x
-y
* (16)9x
2-y
2=(3x
)2-&y
*2 (16)9x
2-y
2=&3x
+y
*&3x
-3y
* 4 3 4 9 16 3 4 9 16 2 3 2 3 4 9 2 3 4 9 1 5 1 5 1 5 1 25 1 4 1 4 1 4 1 16 1 2 1 2 1 2 1 4 1 3 1 3 1 3 1 9(17)-16