Pre-Algebra Examples

$36 x^{2} - 100$

Step 1

Factor out the GCF of $4$ from $36 x^{2} - 100$ .

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Step 1.1

Factor out the GCF of $4$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $4$ from the expression $36 x^{2}$ .

$4 (9 x^{2}) - 100$

Step 1.1.2

Factor out the GCF of $4$ from the expression $- 100$ .

$4 (9 x^{2}) + 4 (- 25)$

Step 1.2

Since all the terms share a common factor of $4$ , it can be factored out of each term.

$4 (9 x^{2} - 25)$

Step 2

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

$4 ({(3 x)}^{2} - 25)$

Step 3

Rewrite $25$ as $5^{2}$ .

$4 ({(3 x)}^{2} - 5^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 5$ .

$4 ((3 x + 5) (3 x - 5))$