Precalculus Examples

$625 x^{4} - 16$

Step 1

Rewrite $625 x^{4}$ as ${(25 x^{2})}^{2}$ .

${(25 x^{2})}^{2} - 16$

Step 2

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

${(25 x^{2})}^{2} - 4^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 25 x^{2}$ and $b = 4$ .

$(25 x^{2} + 4) (25 x^{2} - 4)$

Step 4

Simplify.

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Step 4.1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$(25 x^{2} + 4) ({(5 x)}^{2} - 4)$

Step 4.2

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

$(25 x^{2} + 4) ({(5 x)}^{2} - 2^{2})$

Step 4.3

Factor.

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Step 4.3.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x$ and $b = 2$ .

$(25 x^{2} + 4) ((5 x + 2) (5 x - 2))$

Step 4.3.2

Remove unnecessary parentheses.

$(25 x^{2} + 4) (5 x + 2) (5 x - 2)$