Question

因式分解 ①3(y-x)²+2(x-y)

②4a(x-2)²-2b(2-x)³

③6x³y（x-y）³-4xy³（y-x）²

④a（x-y）-b(y-x)+c(x-y)

⑤m²（x-2）+(2-x)

Answer 1

①3(y-x)²+2(x-y)
=3(x-y)²+2(x-y)
=(x-y)(3x-3y+2)
②4a(x-2)²-2b(2-x)³

=4a(x-2)²+2b(x-2)³

=(x-2)²[4a+2b(x-2)]

=(x-2)²(4a+2bx-4b)
③6x³y（x-y）³-4xy³（y-x）²

=6x³y（x-y）³-4xy³（x-y）²

=(6x³y-4xy³)（x-y）²

=2xy(3x² -2y² )(x-y)²
④a（x-y）-b(y-x)+c(x-y)

=a（x-y）+b(x-y)+c(x-y)

=(x-y)(a+b+c)
⑤m²（x-2）+(2-x)

=(m²-1)（x-2）

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

Answer 2

3(y-x)²+2(x-y)=3(x-y)²+2(x-y)=(x-y)[3(x-y)+2]=(x-y)(3x-3y+2)
4a(x-2)²-2b(2-x)³=4a(x-2)²+2b(x-2)³=2(x-2)²[2a+b(x-2)]=(x-2)²(2a+bx-2b)
6x³y（x-y）³-4xy³（y-x）²=6x³y（x-y）³-4xy³（x-y）²=2xy(x-y)²[3x²(x-y)-2y²]=2xy(x-y)²(3x³-3x²y-2y²

Answer 3

3(y-x)²+2(x-y)=(x-y)(-3(y-x)+2)=(x-y)(3x-3y+2)
4a(x-2)²-2b(2-x)³=(x-2)²(4a+2b(x-2))=(x-2)²(4a+2bx-4b)
6x³y（x-y）³-4xy³（y-x）²=4xy(x²(x-y)²-y²(y-x)²)=4xy(x-y)²(x²-y²)=4xy(x-y)²(x-y)(x+y)
a（x-y）-b(y-x)+c(x-y)=(a+b+c)(x-y)
m²（x-2）+(2-x)=(m²-1)(x-2)