Factor 18a^2-50

$18 a^{2} - 50$

Step 1

Factor $2$ out of $18 a^{2} - 50$ .

Factor $2$ out of $18 a^{2}$ .

$2 (9 a^{2}) - 50$

Factor $2$ out of $- 50$ .

$2 (9 a^{2}) + 2 (- 25)$

Factor $2$ out of $2 (9 a^{2}) + 2 (- 25)$ .

$2 (9 a^{2} - 25)$

Step 2

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

$2 ({(3 a)}^{2} - 25)$

Step 3

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

$2 ({(3 a)}^{2} - 5^{2})$

Step 4

Factor.

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

$2 ((3 a + 5) (3 a - 5))$

Remove unnecessary parentheses.

$2 (3 a + 5) (3 a - 5)$