Question

大哥们，帮帮忙，做一道数学题！过程必须写！

请你试用分组分解法分解因式：x^3-x^2y-xy^2+y^3

Answer 1

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

你看看对不对。嘿嘿。

Answer 2

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

Answer 3

一般都是要把相同的字母提出来的，而且三次方及以上（高次幂的）都要用几个平方或常数的乘积表示出来的。。。所以就把x^2和y^2先提出来
原式=x^2(x-y)-y^2(x-y)
接下来就很明显了。。。提取公因式嘛
=（x-y)(x^2-y^2)
又有平方差公式
=(x+y)(x-y)(x-y)
=(x+y)(x-y)^2