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

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

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

(x+y)^2(x-y)^2-(x+y)(x-y)(x^2+y^2) 用完全平方公式计算
原式=[(x+y)(x-y)]²-(x²-y²)(x²+y²)
=(x²-y²)²-(x⁴-y⁴)
=x⁴-2x²y²+y⁴-x⁴+y⁴
=-2x²y²+2y⁴

=[(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

(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)