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x^6-y^6+3x^2y^4-3x^4y2
题目详情
x^6-y^6+3x^2y^4-3x^4y2
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答案和解析
解x^6-y^6+3x^2y^4-3x^4y2
=(x^2)^6-(y^2)^6+3x^2y^4-3x^4y2
=(x^2-y^2)(x^4+x^2y^2+y^4)+3x^2y^2(y^2-x^2)
=(x^2-y^2)(x^4+x^2y^2+y^4)-3x^2y^2(x^2-y^2)
=(x^2-y^2)[(x^4+x^2y^2+y^4)-3x^2y^2]
=(x^2-y^2)(x^4-2x^2y^2+y^4)
=(x^2-y^2)(x^2-y^2)^2
=(x^2-y^2)^3
=(x^2)^6-(y^2)^6+3x^2y^4-3x^4y2
=(x^2-y^2)(x^4+x^2y^2+y^4)+3x^2y^2(y^2-x^2)
=(x^2-y^2)(x^4+x^2y^2+y^4)-3x^2y^2(x^2-y^2)
=(x^2-y^2)[(x^4+x^2y^2+y^4)-3x^2y^2]
=(x^2-y^2)(x^4-2x^2y^2+y^4)
=(x^2-y^2)(x^2-y^2)^2
=(x^2-y^2)^3
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