因式分解：1.(x-2y)^2-4y^2

题目

因式分解：1.(x-2y)^2-4y^2
2.32(a-b)^2-18(a+b)^2
3.9a^2-2a+1/9
4.(a+2b)^2+(8a+2b)+16
5.x^2y^2-5xy+6
6.x^3-8x^2+15
7.ax+ay-bx-by
8.a^2-a-b^2+b
9.x^2-2xy+y^2-z^2
10.(2x+3y-3)(2x+3y+7)-11
11.4x^2-12xy+9y^2-2x+3y-6

答案

1.(x-2y)^2-4y^2=(x-2y+2y)(x-2y-2y)=x(x-4y)
2.32(a-b)^2-18(a+b)^2=2[4(a-b)+3(a+b)][4(a-b)-3(a+b)]=2(7a-b)(a-7b)
3.9a^2-2a+1/9=(3a-1/3)²
4.(a+2b)^2+8(a+2b)+16=(a+2b+4)²
5.x^2y^2-5xy+6=(xy-3)(xy-2)
6.x^3-8x^2+15x=x(x-3)(x-5)
7.ax+ay-bx-by=a(x+y)-b(x+y)=(a-b)(x+y)
8.a^2-a-b^2+b=(a+b)(a-b)-(a-b)=(a-b)(a+b-1)
9.x^2-2xy+y^2-z^2=(x-y)²-z²=(x-y+z)(x-y-z)
10.(2x+3y-3)(2x+3y+7)-11=(2x+3y-3)²+10(2x+3y-3)-11=(2x+3y+8)(2x+3y-4)
11.4x^2-12xy+9y^2-2x+3y-6=(2x-3y)²-(2x-3y)-6=(2x-3y-3)(2x-3y+2)