分解公因式
问题描述：
分解公因式
p(x-y)-q(y-x)
(a+b)(a-b)-(b+a)
10a(x-y)^2-5b(y-x)
3p(m-2n)-(2n-m)^2
4(m-n)^2-12n(n-m)^2
(a+b)^(m-1)-(a+b)^m
答
p(x-y)-q(y-x)
=p(x-y)+q(x-y)
=(p+q)(x-y)
(a+b)(a-b)-(b+a)
=(a+b)(a-b-1)
10a(x-y)^2-5b(y-x)
=10a(x-y)^2+5b(x-y)
=5(x-y)(2ax-2ay+bx-by)
=5(x-y)[2a(x-y)+b(x-y)]
=5(x-y)^2(2a+b)
3p(m-2n)-(2n-m)^2
=-[3p(2n-m)+(2n-m)^2]
=-(2n-m)(3p+2n-m)
4(m-n)^2-12n(n-m)^2
=4(n-m)^2-12n(n-m)^2
=4(n-m)^2(1-3n)
(a+b)^(m-1)-(a+b)^m
=(a+b)^(m-1)-(a+b)^(m-1)*(a+b)
=(a+b)^(m-1)(1-a-b)