Pre-Algebra Examples

$a^{3} + b^{6}$

Step 1

Rewrite $b^{6}$ as ${(b^{2})}^{3}$ .

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

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 $a = a$ and $b = b^{2}$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

$(a + b^{2}) (a^{2} - a b^{2} + b^{4})$