Algebra Examples

$16 - x^{4}$

Step 1

Rewrite $16$ as $4^{2}$ .

$4^{2} - x^{4}$

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

Rewrite $4$ as $2^{2}$ .

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

Step 4.2

Factor.

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Step 4.2.1

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

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

Step 4.2.2

Remove unnecessary parentheses.

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