How do you factor $x^3y^3 + z^3$ ?

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Answer 1 · 2015-07-22T07:39:48

Use sum of cubes identity to find:

$x^3y^3+z^3 = (xy+z)(x^2y^2-xyz+z^2)$

Use the sum of cubes identity:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

with $a=xy$ and $b=z$ as follows:

$x^3y^3+z^3$

$=(xy)^3+z^3$

$=((xy)+z)((xy)^2-(xy)z+z^2)$

$=(xy+z)(x^2y^2-xyz+z^2)$

How do you factor x^3y^3 + z^3x^3y^3 + z^3?