（x+2y)²(x-2y)²-(2x+y)²(2x-y)²可以化简成什么?

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/08/02 01:08:39

(x+2y)²(x-2y)²-(2x+y)²(2x-y)²
=[(x+2y)(x-2y)]²-[(2x+y)(2x-y)]²
=(x^2-4y^2)^2 - (4x^2-y^2)^2
=(x^2-4y^2 + 4x^2-y^2) * ( x^2-4y^2 - 4x^2+y^2 )
=(5x^2-5y^2)*(-3x^2-3y^2)
=5(x^2-y^2)*(-3)(x^2+y^2)
=-15(x+y)(x-y)(x^2+y^2)

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