Question

因式分解x^3-y^3-x(x^2-y^2)+y(x-y)^2要详细的步骤

Answer 1

【参考答案】

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

注意：立方差正确公式为：x^3 -y^3=(x-y)(x^2 +xy+y^2)

满意记得采纳，不理解欢迎追问。。

Answer 2

原式=(x-y)(x²+2xy+y²)-x(x+y)(x-y)+y(x-y)²
=(x-y)[(x²+2xy+y²)-x(x+y)+y(x-y)]
=(x-y)(x²+2xy+y²-x²-xy+xy-y²)
=2xy(x-y)