【急!因式分解】用配方法做!!
x^2-2(a+b)x-ab(a-2)(b+2)x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2...
x^2-2(a+b)x-ab(a-2)(b+2)
x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2 展开
x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2 展开
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1.x^2-2(a+b)x-ab(a-2)(b+2)
=[x+b(a-2)][x-a(b+2)]
2.x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2
=x^4-2x^2y^2+y^4-2y^2z^2-2z^2x^2+z^4
=(x^2-y^2)^2-2z^2(x^2+y^2)+z^4
=(x^2-y^2)^2-2z^2(x^2-y^2)+z^4-4y^2z^2
=(x^2-y^2-z^2)^2-4y^2z^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+b(a-2)][x-a(b+2)]
2.x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2
=x^4-2x^2y^2+y^4-2y^2z^2-2z^2x^2+z^4
=(x^2-y^2)^2-2z^2(x^2+y^2)+z^4
=(x^2-y^2)^2-2z^2(x^2-y^2)+z^4-4y^2z^2
=(x^2-y^2-z^2)^2-4y^2z^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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