Question

(x+y)的三次方(x-y)的二次方-(x-y)(x+y)(x的二次方+y的二次方)

急~明天就要用,我要的是过程,不是结果,过程要明确
100分呢,高手进
对不起,我打错了,题目应该是(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)

Answer 1

问题疑为：(x+y)^3(x-y)^2-(x+y)(x-y)(x^2-y^2)
(x+y)^3(x-y)^2-(x+y)(x-y)(x^2-y^2)
=(x+y)^3(x-y)^2-(x+y)^2(x-y)^3
=(x+y)^2(x-y)^2[x+y-x+y]
=2y(x+y)^2(x-y)^2

追问

对不起,我打错了,题目应该是(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
麻烦你能再帮我看一下吗,我会再追加给你分数的
O(∩_∩)O谢谢

Answer 2

(x+y)^3(x-y)^2-(x-y)(x+y)(x^2+y^2)
= (x+y)^3(x-y)^2-(x^2-y^2)(x^2+y^2)
=(x+y)(x+y)^2(x-y)^2-(x^2-y^2)(x^2+y^2)
=(x+y)(x^2-y^2)^2-(x^2-y^2)(x^2+y^2)
=(x^2-y^2){(x+y)(x^2-y^2)-(x^2+y^2)}
=(x+y)(x-y){(x+y)(x^2-y^2)-(x^2+y^2)}

追问

对不起,我打错了,题目应该是(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
麻烦你能再帮我看一下吗,我会再追加给你分数的
O(∩_∩)O谢谢

追答

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

Answer 3

(x+y)^2(x-y)^2-(x-y)(x+y)(x^2+y^2)
=(x+y)(x-y)[(x+y)(x-y)-(x^2+y^2)]
=(x+y)(x-y)[x^2-y^2-x^2-y^2]
=-2y^2(x+y)(x-y)

Answer 4

= x^4+y^4-2x^2 y^2-x^4+y^4
= 2y^4- 2x^2 y^2