问题: 因式分解
4x^2+3z-3xz-4x
x^2-y^2-z^2+2yz
x^3-x^2y-xy^2+y^2
x^2+4x+3
解答:
4x^2+3z-3xz-4x
=4x^2-3xz-4x+3z
=x(4x-3z)-(4x-3z)
=(4x-3z)(x-1)
x^2-y^2-z^2+2yz
=x^2-(y^2+z^2-2yz )
=x^2-(y-z)^2
=[x+(y-z)][x-(y-z)]
=(x+y-z)(x-y+z)
x^3-x^2y-xy^2+y^3
=x^2(x-y)-y^2(x-y)
=(x-y)(x^2-y^2)
=(x-y)(x+y)(x-y)
=(x+y)(x-y)^2
x^2+4x+3
=(x+3)(x+1)
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