Question

因式分解：b-a+c(a-b)

（1）b-a+c(a-b)；（2）m(a²+b²）+n(a²+b²）；（3）x(x+y)(x-y)-x(x+y)²;
(4)2(y-x)²+3(x-y);(5)mn(m-n)-m(n-m)³；（6）a(b-3)²+2(b-3)²
(7)(x-y)³+(x-y)²-(y-x);(8)a(m-2)+b(2-m);(9)2(y-x)²+3(x-y)

Answer 1

b-a+c(a-b)
=b-a-c(b-a)
=(b-a)(1-c)

m(a²+b²）+n(a²+b²）
=(a²+b²)(m+n)

x(x+y)(x-y)-x(x+y)²
=x(x+y)(x-y-x-y)
=-2xy(x+y)

2(y-x)²+3(x-y)
=2(x-y)²+3(x-y)
=(x-y)(2x-2y+3)

mn(m-n)-m(n-m)³
=mn(m-n)+m(m-n)³
=m(m-n)(n+m²-2mn+n²)

a(b-3)²+2(b-3)²
=(b-3)²(a+2)

(x-y)³+(x-y)²-(y-x)
=(x-y)[(x-y)²+(x-y)+1]
=(x-y)(x²-2xy+y²+x-y+1)

a(m-2)+b(2-m)
=a(m-2)-b(m-2)
=(m-2)(a-b)

2(y-x)²+3(x-y)
=2(x-y)²+3(x-y)
=(x-y)(2x-2y+3)