把下列各式分解因式,要有具体过程的!x(x-y)^2-y(y-x)^218(a-b)^3-12b(b-a)^2(2a+b)(2a-3b)-3a(2a+b)x(x+3)(x-y)-x(x+y)^2

Question

把下列各式分解因式,要有具体过程的!
x(x-y)^2-y(y-x)^2
18(a-b)^3-12b(b-a)^2
(2a+b)(2a-3b)-3a(2a+b)
x(x+3)(x-y)-x(x+y)^2

Answer 1

1.x(x-y)^2-y(y-x)^2 = (x-y)^2*(x-y)
= (x-y)^3
2.18(a-b)^3-12b(b-a)^2 = (a-b)^2*(18a-18b-12b)
= 6(a-b)^2*(3a-5b)
3.(2a+b)(2a-3b)-3a(2a+b) = (2a+b)(2a-3b-3a)
= -(2a+b)(a+3b)
4.x(x+3)(x-y)-x(x+y)^2 = x(x^2+3x-3y-xy-x^2-2xy-y^2)
= x(3x-3y-3xy-y^2)