Basic Math Examples

$a^{3} b^{3} - c^{9}$

Step 1

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

${(a b)}^{3} - c^{9}$

Step 2

Rewrite $c^{9}$ as ${(c^{3})}^{3}$ .

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

Step 3

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 $b = c^{3}$ .

$(a b - c^{3}) ({(a b)}^{2} + a b c^{3} + {(c^{3})}^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the product rule to $a b$ .

$(a b - c^{3}) (a^{2} b^{2} + a b c^{3} + {(c^{3})}^{2})$

Step 4.2

Multiply the exponents in ${(c^{3})}^{2}$ .

Tap for more steps...

Step 4.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$(a b - c^{3}) (a^{2} b^{2} + a b c^{3} + c^{3 \cdot 2})$

Step 4.2.2

Multiply $3$ by $2$ .

$(a b - c^{3}) (a^{2} b^{2} + a b c^{3} + c^{6})$