Question

分解因式（x-y)(x平方+xy+y平方)-xy(y-x)

要过程

Answer 1

（x-y)(x^2+xy+y^2)-xy(y-x)
原式=（x-y)(x^2+xy+y^2)+xy(x-y) ……改变符号
=(x-y)(x^2+2xy+y^2) ……提取公因式
=（x-y)(x+y)^2

Answer 2

=(x-y)(x²+xy+y²)+xy(x-y)
=(x-y)(x²+2xy+y²)
=(x-y)(x+y)²

Answer 3

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

Answer 4

解释： 先看后面的，将它乘出来。就是-xy²+x²y，提取xy就是xy(x-y).这时候就会发现前面一项也有(x-y),就提出来，=（x-y)(xy+xy+x²+y²)=（x-y)(2xy+x²+y²).而根据公式a²+2ab+b²=（a+b)²，可得)(2xy+x²+y²)=（x+y)²，所以结果为（x-y)(x+y)²。这样就可以写了。
原式=（x-y)(x²+xy+y²）+xy(x-y)
=（x-y))(xy+xy+x²+y²)-----这步可以省
=(x-y)(2xy+x²+y²)
=（x-y)(x+y)²
有不懂得可以问我，419365095

Answer 5

这个最好要记住的啦
x³-y³=(x-y)(x²+xy+y²)
用-y换y，又可以得到
x³+y³=(x+y)(x²--xy+y²)