因式分解 x^3-2x2y+xy^2 a^3b+ab^3 1/3-3A^2 (x+y)^2-4(x+y-1) -x^2y+2xy^2-y^3
题目
因式分解 x^3-2x2y+xy^2 a^3b+ab^3 1/3-3A^2 (x+y)^2-4(x+y-1) -x^2y+2xy^2-y^3
答案
x^3-2x2y+xy^2
=x(x^2-2xy+y^2)
=x(x-y)^2
a^3b+ab^3
=ab(a^2+b^2)
1/3-3A^2
=1/3(1-9A^2)
=1/3(1+3A)(1-3A)
(x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y-2)^2
-x^2y+2xy^2-y^3
= -y(x^2-2xy+y^2)
=-y(x-y)^2
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