Finite Math Examples

$1 - 16 x^{12}$

Step 1

Rewrite $1$ as $1^{2}$ .

$1^{2} - 16 x^{12}$

Step 2

Rewrite $16 x^{12}$ as ${(4 x^{6})}^{2}$ .

$1^{2} - {(4 x^{6})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 4 x^{6}$ .

$(1 + 4 x^{6}) (1 - (4 x^{6}))$

Step 4

Simplify.

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Step 4.1

Remove parentheses.

$(1 + 4 x^{6}) (1 - 1 \cdot 4 x^{6})$

Step 4.2

Rewrite $1$ as $1^{2}$ .

$(1 + 4 x^{6}) (1^{2} - 1 \cdot 4 x^{6})$

Step 4.3

Rewrite $4 x^{6}$ as ${(2 x^{3})}^{2}$ .

$(1 + 4 x^{6}) (1^{2} - {(2 x^{3})}^{2})$

Step 4.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 2 x^{3}$ .

$(1 + 4 x^{6}) ((1 + 2 x^{3}) (1 - (2 x^{3})))$

Step 4.5

Factor.

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Step 4.5.1

Multiply $2$ by $- 1$ .

$(1 + 4 x^{6}) ((1 + 2 x^{3}) (1 - 2 x^{3}))$

Step 4.5.2

Remove unnecessary parentheses.

$(1 + 4 x^{6}) (1 + 2 x^{3}) (1 - 2 x^{3})$