Algebra Examples

$405 x^{4} - 5 x^{2}$

Step 1

Factor out the GCF of $5 x^{2}$ from $405 x^{4} - 5 x^{2}$ .

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Step 1.1

Factor out the GCF of $5 x^{2}$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $5 x^{2}$ from the expression $405 x^{4}$ .

$5 x^{2} (81 x^{2}) - 5 x^{2}$

Step 1.1.2

Factor out the GCF of $5 x^{2}$ from the expression $- 5 x^{2}$ .

$5 x^{2} (81 x^{2}) + 5 x^{2} (- 1)$

Step 1.2

Since all the terms share a common factor of $5 x^{2}$ , it can be factored out of each term.

$5 x^{2} (81 x^{2} - 1)$

Step 2

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

$5 x^{2} ({(9 x)}^{2} - 1)$

Step 3

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

$5 x^{2} ({(9 x)}^{2} - 1^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 x$ and $b = 1$ .

$5 x^{2} ((9 x + 1) (9 x - 1))$