数学题-分解因式

Question

把下列各式分解因式(^2为平方，^3为立方）
1.mn(a^2+b^2)+mn^2(a^2+b^2)
2.x(x+y)(x-y)-x(x+y)^2(x-y)
3.x(m-n)^3-x^2(n-m)^2
4.4m(x-y)-2m^2(y-x)^3
这些我不太会帮忙解一下，过程写清楚，否则我看不懂，谢谢！

Answer 1

1.mn(a^2+b^2)+mn^2(a^2+b^2)
提取公因式mn(a^2+b^2)
=mn(a^2+b^2)(1+n)

2.x(x+y)(x-y)-x(x+y)^2(x-y)
提取公因式x(x+y)(x-y)
=x(x+y)(x-y)[1-(x+y)]
=x(x+y)(x-y)(1-x-y)

3.x(m-n)^3-x^2(n-m)^2
=x(m-n)^3-x^2(m-n)^2
提取公因式x(m-n)^2
=x(m-n)^2[(m-n)-x]
=x(m-n)^2(m-n-x)

4.4m(x-y)-2m^2(y-x)^3
=4m(x-y)+2m^2(x-y)^3
提取公因式2m(x-y)
=2m(x-y)[2-m(x-y)^2]
=2m(x-y)(2-mx^2+2mxy-my^2)

Answer 2

1.mn(a^2+b^2)+mn^2(a^2+b^2)
=mn(a^2+b^2)(n+1)

2.x(x+y)(x-y)-x(x+y)^2(x-y)
=x(x+y)(x-y)(1-x-y)

3.x(m-n)^3-x^2(n-m)^2
=x(n-m)^2 (m-n-x)

4.4m(x-y)-2m^2(y-x)^3
=4m(x-y)+2m^2(x-y)^3
=2m(x-y)(2+mx^2+my^2-2mxy)