Algebra Examples

$64 + a^{6}$

Step 1

Rewrite $64$ as $4^{3}$ .

$4^{3} + a^{6}$

Step 2

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

$4^{3} + {(a^{2})}^{3}$

Step 3

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 $a = 4$ and $b = a^{2}$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Raise $4$ to the power of $2$ .

$(4 + a^{2}) (16 - 4 a^{2} + {(a^{2})}^{2})$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$(4 + a^{2}) (16 - 4 a^{2} + a^{2 \cdot 2})$

Step 4.2.2

Multiply $2$ by $2$ .

$(4 + a^{2}) (16 - 4 a^{2} + a^{4})$