Algebra Examples

$x^{3} y^{3} + z^{3}$

Step 1

Rewrite $x^{3} y^{3}$ as ${(x y)}^{3}$ .

${(x y)}^{3} + z^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x y$ and $b = z$ .

$(x y + z) ({(x y)}^{2} - (x y) z + z^{2})$

Step 3

Simplify.

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Step 3.1

Apply the product rule to $x y$ .

$(x y + z) (x^{2} y^{2} - (x y) z + z^{2})$

Step 3.2

Remove parentheses.

$(x y + z) (x^{2} y^{2} - x y z + z^{2})$