提取公因数——平方差公式法(1)(x+y)^3(x-y)-(x+y)(x-y)^3(2)25(x-2y)^3+4(2y-x)
问题描述：
提取公因数——平方差公式法
(1)(x+y)^3(x-y)-(x+y)(x-y)^3
(2)25(x-2y)^3+4(2y-x)
答
1题 (x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x^2-y^2)(x^2+2xy+y^2-x^2+2xy-y^2)
=4xy(x^2-y^2)
=4x^3y-4xy^3
2题 25(x-2y)^3+4(2y-x)
=25(x-2y)^3-4(x-2y)
=(x-2y)[25(x-2y)^2-4]
=(x-2y)[25(x^2+4y^2-4xy)-4]
没时间了,后面的自己算!
答
题1(x+y)^3(x-y)-(x+y)(x-y)^3=(x+y)(x-y)[(x+y)^2-(x-y)^2]=(x^2-y^2)(x^2+2xy+y^2-x^2+2xy-y^2)=4xy(x^2-y^2)=4xy(x+y)(x-y)题225(x-2y)^3+4(2y-x)=25(x-2y)^3-4(x-2y)=(x-2y)[25(x-2y)^2-4]=(x-2y)[5(x-2y)+2][5(...