Question

(1) a²x²y-axy² (2) x(x-y)-（y-x） (3) m(x-y) ²-x+y (4)9(a-b) ²-16(a+b)&sup

分解因式

Answer 1

(1)原式=axy*(ax-y)
(2)原式=x(x-y)+(x-y)=(x-y)(x+1)
(3)原式=m(x-y)^2-(x-y)=(x-y)[m(x-y)-1]
(4)原式=[3(a-b)]^2-[4(a+b)]^2=[3(a-b)+4(a+b)]*[3(a-b)-4(a+b)]=-(7a+b)(a+7b)

Answer 2

（1）a²x²y-axy² =axy（ax-y）
（2）x(x-y)-（y-x）=x（x-y）+（x-y）=（x-y）（x+1）
（3）m(x-y) ²-x+y=m(x-y) ²-（x-y）=（x-y）（mx-my-1）
（4）9(a-b) ²-16(a+b) ²=[3(a-b)]²-[4(a+b)]²=[3(a-b)+4(a+b)][3(a-b)-4(a+b)]=-(7a+b)(a+7b)

Answer 3

a²x²y-axy²
=axy(ax-y)

x(x-y)-(y-x)
=x(x-y)-(x-y)
=(x-y)(x-1)

m(x-y) ²-x+y
=m(x-y) ²-(x-y)
=(x-y)(m(x-y)-1)

9(a-b) ²-16(a+b)^2
=(3a-3b)^2-(4a+4b)^2
=(3a-3b+4a+4b)(3a-3b-4a-4b)
=(7a-b)(-a-7b)