Algebra Examples

9 x^{2} - 36

$9 x^{2} - 36$

Step 1

Factor

9

$9$ out of

9 x^{2} - 36

$9 x^{2} - 36$ .

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Step 1.1

Factor

9

$9$ out of

9 x^{2}

$9 x^{2}$ .

9 (x^{2}) - 36

$9 (x^{2}) - 36$

Step 1.2

Factor

9

$9$ out of

- 36

$- 36$ .

9 x^{2} + 9 \cdot - 4

$9 x^{2} + 9 \cdot - 4$

Step 1.3

Factor

9

$9$ out of

9 x^{2} + 9 \cdot - 4

$9 x^{2} + 9 \cdot - 4$ .

9 (x^{2} - 4)

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

9 (x^{2} - 4)

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

Step 2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 2

$b = 2$ .

9 ((x + 2) (x - 2))

$9 ((x + 2) (x - 2))$

Step 3.2

Remove unnecessary parentheses.

9 (x + 2) (x - 2)

$9 (x + 2) (x - 2)$

9 (x + 2) (x - 2)

$9 (x + 2) (x - 2)$