Algebra Examples

$8 x^{2} - 18 y^{2}$

Step 1

Factor $2$ out of $8 x^{2} - 18 y^{2}$ .

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Step 1.1

Factor $2$ out of $8 x^{2}$ .

$2 (4 x^{2}) - 18 y^{2}$

Step 1.2

Factor $2$ out of $- 18 y^{2}$ .

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

Step 1.3

Factor $2$ out of $2 (4 x^{2}) + 2 (- 9 y^{2})$ .

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

Step 2

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Factor.

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Step 5.1

Multiply $3$ by $- 1$ .

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

Step 5.2

Remove unnecessary parentheses.

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