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factor x^3-(x+y)^3

• please, need help on factoring -

in general
a^3-b^3 = (a-b)(a^2 + a b + b^2)
so
(x-x-y)(x^2+x^2+xy +x^2+2xy+y^2)
-y ( 3x^2+3xy+y^2)

• please, need help on factoring -

If you multiply out (x+y)^3 and subtract it, you get rid of the x^3 terms, and then factor out y.

x^3 -(x^3 + 3x^2y + 3xy^2 +y^3)
= -y(3x^2 + 3xy + y^2)

The term in parentheses does not factor with integer coefficients.

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