Precalculus Examples

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

Step 1

Factor $x^{2}$ out of $4 x^{2} - x^{4}$ .

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Step 1.1

Factor $x^{2}$ out of $4 x^{2}$ .

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

Step 1.2

Factor $x^{2}$ out of $- x^{4}$ .

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

Step 1.3

Factor $x^{2}$ out of $x^{2} \cdot 4 + x^{2} (- x^{2})$ .

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

Step 2

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

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

Step 3

Factor.

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Step 3.1

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

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

Step 3.2

Remove unnecessary parentheses.

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