Finite Math Examples

$8 x^{6} + 64$

Step 1

Factor $8$ out of $8 x^{6} + 64$ .

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Step 1.1

Factor $8$ out of $8 x^{6}$ .

$8 (x^{6}) + 64$

Step 1.2

Factor $8$ out of $64$ .

$8 x^{6} + 8 \cdot 8$

Step 1.3

Factor $8$ out of $8 x^{6} + 8 \cdot 8$ .

$8 (x^{6} + 8)$

Step 2

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

$8 ({(x^{2})}^{3} + 8)$

Step 3

Rewrite $8$ as $2^{3}$ .

$8 ({(x^{2})}^{3} + 2^{3})$

Step 4

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

$8 ((x^{2} + 2) ({(x^{2})}^{2} - x^{2} \cdot 2 + 2^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

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Step 5.1.1.1

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

$8 ((x^{2} + 2) (x^{2 \cdot 2} - x^{2} \cdot 2 + 2^{2}))$

Step 5.1.1.2

Multiply $2$ by $2$ .

$8 ((x^{2} + 2) (x^{4} - x^{2} \cdot 2 + 2^{2}))$

Step 5.1.2

Multiply $2$ by $- 1$ .

$8 ((x^{2} + 2) (x^{4} - 2 x^{2} + 2^{2}))$

Step 5.1.3

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

$8 ((x^{2} + 2) (x^{4} - 2 x^{2} + 4))$

Step 5.2

Remove unnecessary parentheses.

$8 (x^{2} + 2) (x^{4} - 2 x^{2} + 4)$