Algebra Examples

2 x^{2} - 18

$2 x^{2} - 18$

Step 1

Factor

2

$2$ out of

2 x^{2} - 18

$2 x^{2} - 18$ .

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Step 1.1

Factor

2

$2$ out of

2 x^{2}

$2 x^{2}$ .

2 (x^{2}) - 18

$2 (x^{2}) - 18$

Step 1.2

Factor

2

$2$ out of

- 18

$- 18$ .

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

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

Step 1.3

Factor

2

$2$ out of

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

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

2 (x^{2} - 9)

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

2 (x^{2} - 9)

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

Step 2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

2 (x^{2} - 3^{2})

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

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 = 3

$b = 3$ .

2 ((x + 3) (x - 3))

$2 ((x + 3) (x - 3))$

Step 3.2

Remove unnecessary parentheses.

2 (x + 3) (x - 3)

$2 (x + 3) (x - 3)$

2 (x + 3) (x - 3)

$2 (x + 3) (x - 3)$