# How do you factor the expression x^3y^3 + z^3?

Feb 7, 2016

Answer is: $\left(x y + z\right) \left({x}^{2} {y}^{2} - x y z + {z}^{2}\right)$.

You can check by multiplying it out.

#### Explanation:

Notice that each term is a perfect cube: ${x}^{3} {y}^{3} = {\left(x y\right)}^{3}$.

So we have a sum of cubes, and the factoring formula is:

${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

So we use $a = x y$ and $b = z$ to get:

${x}^{3} {y}^{3} + {z}^{3} = {\left(x y\right)}^{3} + {z}^{3}$

$= \left(\left(x y\right) + z\right) \left({\left(x y\right)}^{2} - \left(x y\right) z + {z}^{2}\right)$

$= \left(x y + z\right) \left({x}^{2} {y}^{2} - x y z + {z}^{2}\right)$.

check by multiplying it out to make sure!

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