一道初中数学题（要过程）

Question

1.因式分解。（1）.x^4+y^4+z^4-2x^2y^2-2x^2z^2-2z^2y^2

Answer 1

x^4+y^4+z^4-2x²y²-2x²z²-2y²z²
=x^4+y^4+z^4+2x²y²-4x²y²-2x²z²-2y²z² (把-2x²y²æ‹†å¼€)
=(x²+y²-z²)²-4x²y²
=(x²+y²-z²-2xy)(x²+y²-z²+2xy)
=(x-y-z)(x-y+z)(x+y-z)(x+y+z)

由于四次方没有找到符号所以只能那样写了，呵呵。

Answer 2

x^4+y^4+z^4-2x^2y^2-2x^2z^2-2z^2y^2
=x^4+y^4+z^4+2x^2y^2-2x^2z^2-2z^2y^2-4x^2y^2
=(x^4+2x^2y^2+y^4)-2z^2(x^2+y^2)+z^4-4x^2y^2
=[(x^2+y^2)^2-2z^2(x^2+y^2)+z^4]-4x^2y^2
=[(x^2+y^2)-z^2]^2-4x^2y^2
=[(x^2+y^2)-z^2+2xy][(x^2+y^2)-z^2-2xy]
=[(x+y)^2-z^2][(x-y)^2-z^2]
=(x+y+z)(x+y-z)(x-y+z)(x-y-z)