Algebra Examples

$a^{3} b^{3} - x^{3}$

Step 1

Rewrite $a^{3} b^{3}$ as ${(a b)}^{3}$ .

${(a b)}^{3} - x^{3}$

Step 2

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

$(a b - x) ({(a b)}^{2} + a b x + x^{2})$

Step 3

Apply the product rule to $a b$ .

$(a b - x) (a^{2} b^{2} + a b x + x^{2})$