(X^2-Y^2+Z^2)^2-4X^2Z^2
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![(X^2-Y^2+Z^2)^2-4X^2Z^2](/uploads/image/z/7123751-71-1.jpg?t=%28X%5E2-Y%5E2%2BZ%5E2%29%5E2-4X%5E2Z%5E2)
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(X^2-Y^2+Z^2)^2-4X^2Z^2
(X^2-Y^2+Z^2)^2-4X^2Z^2
(X^2-Y^2+Z^2)^2-4X^2Z^2
原式
=[(x^2-2xz+z^2)-y^2][(x^2+2xz+y^2)-y^2]
=[(x-z)^2-y^2][(x+z)^2-y^2]
=(x-z+y)(x-z-y)(x+y+z)(x-y+z)
狂用平方差公式
=x^4+y^4+z^4-2x^2y^2-2y^2z^2+2x^2z^2-4x^2z^2
=x^4+y^4+z^4-2x^2y^2-2y^2z^2-2x^2z^2
这里是既约的吧?
x^4+y^4+z^4+2x^2y^2+2y^2z^2+2x^2z^2倒可以分:
(X^2+Y^2+Z^2)^2
=(x-z+y)(x-z-y)(x+y+z)(x-y+z)
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