Question

数学问题（完全平方公式）八年级

2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=-(x-y)²(x-y)²-(x-y)(x+y)(x²+y²)①
=-(x-y)^4-[(x²-y²)(x²+y²)]②
=-（x-y)^4-[x^4-y^4]③
对不对，如果对，怎么继续做，如果错了，哪里错了，第几步，请改正

Answer 1

第一步错了！
=（x+y）（x-y)【（x+y）（x-y）-x^2-y^2】
祝你学习进步！！
望采纳！

Answer 2

　　解：第①步错了
　　(x+y)²≠-(x-y)²！

　　改正：
　　(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
　　=[(x+y)(x-y)]²-(x-y)(x+y)(x²+y²)①
　　=[(x²-y²)]²-[(x²-y²)(x²+y²)]②
　　=x^4+y^4-2x²y²-[x^4-y^4]③
　　=x^4+y^4-2x²y²-x^4+y^4
　　=2y^4-2x²y²
　　=2y²(y²-x²)
　　=2y²(x+y)(y-x).

Answer 3

第一步到第二步就错了
第二步应该是[(x+y)(x-y)]^2-(x^2-y^2)(x^2+y^2)
第三步（x^2-y^2)^2-(x^4-y^4)
第四步化开x^4-2x^2y^2+y^4-x^4+y^4
第五步就是结果了

追问

=(x²-y²)²-(x²-y²)(x²+y²)
=（x^4-y^4)-(x^4-y^4)
应该=0啊

Answer 4

2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)

=(x-y)(x+y）[2(x-y)(x+y）-(x²+y²)]
=(x-y)(x+y）[2(x²-y²)-(x²+y²)]
=(x-y)(x+y）(x²-3y²)

追问

我哪里错了

追答

第一步的变化不对
2.(x+y)²(x-y)²≠-(x-y)²(x-y)²

Answer 5

第一步错了 (x+y)²(x-y)²=[(x+y)(x-y)]²=(x²-y²)² 而不是 -(x-y)²(x-y)²

原式=(x²-y²)²-(x-y)(x+y)(x²+y²)
=(x²-y²)[(x²-y²)-(x²+y²)]
=(x²-y²)(-2y²)
=-2(x+y)(x-y)y²
很高兴数学团队【逻辑美】为您解答，祝您学习进步。