【麻烦解几道分解因式的题,4a^2-b^2+6a-3b9m^2-6m+2n-n^2x^2-y^2-z^2+2yzx^3-x^2y-xy^2+y^3】
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问题描述：
麻烦解几道分解因式的题,
4a^2-b^2+6a-3b
9m^2-6m+2n-n^2
x^2-y^2-z^2+2yz
x^3-x^2y-xy^2+y^3
万峻甫回答：
4a^2-b^2+6a-3b=(4a^2+6a)-(b^2+3b)=2a(a+3)+b(b+3)
9m^2-6m+2n-n^2=(9m^2-6m)-(n^2-2n)=3m(3m-2)-n(n-2)
x^2-y^2-z^2+2yz=x^2-(y^2-2yz+z^2)=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^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
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