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分解因式：(x^2-y^2)^2-2z^2(x^2-y^2)+z^4-4y^2z^2
题目详情
分解因式：(x^2-y^2)^2-2z^2(x^2-y^2)+z^4-4y^2z^2
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答案和解析
(x^2-y^2)^2-2z^2(x^2-y^2)+z^4-4y^2z^2
=(x^2-y^2-z^2)^2-(2yz)^2
=(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)
=[x^2-(y-z)^2][x^2-(y+z)^2]
=(x+y-z)(x-y+z)(x+y+z)(x-y-z)
=(x^2-y^2-z^2)^2-(2yz)^2
=(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)
=[x^2-(y-z)^2][x^2-(y+z)^2]
=(x+y-z)(x-y+z)(x+y+z)(x-y-z)
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