Algebra Examples

$(81 x^{4} - 16)$

Step 1

Remove parentheses.

$81 x^{4} - 16$

Step 2

Rewrite $81 x^{4}$ as ${(9 x^{2})}^{2}$ .

${(9 x^{2})}^{2} - 16$

Step 3

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

${(9 x^{2})}^{2} - 4^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 x^{2}$ and $b = 4$ .

$(9 x^{2} + 4) (9 x^{2} - 4)$

Step 5

Simplify.

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Step 5.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$(9 x^{2} + 4) ({(3 x)}^{2} - 4)$

Step 5.2

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

$(9 x^{2} + 4) ({(3 x)}^{2} - 2^{2})$

Step 5.3

Factor.

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Step 5.3.1

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

$(9 x^{2} + 4) ((3 x + 2) (3 x - 2))$

Step 5.3.2

Remove unnecessary parentheses.

$(9 x^{2} + 4) (3 x + 2) (3 x - 2)$