（x+y)^2（x-y)^2-(x+y)(x-y)(x^2+y^2) 用完全平方公式计算

分类: 作业答案 • 2021-12-19 11:37:07

问题描述：

答

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

答

=[(x+y)(x-y)]²-(x²-y²)(x²+y²)
=(x²-y²)²-(x的4次方-y的4次方)
=x的4次方-2x²y²+y的4次方-x的4次方+y的4次方
=-2x²y²+2y的4次方

答

原式=[(x+y)(x-y)]²-(x²-y²)(x²+y²)
=(x²-y²)²-(x⁴-y⁴)
=x⁴-2x²y²+y⁴-x⁴+y⁴
=-2x²y²+2y⁴