Factor 20x^2-45

$20 x^{2} - 45$

Step 1

Factor $5$ out of $20 x^{2} - 45$ .

Factor $5$ out of $20 x^{2}$ .

$5 (4 x^{2}) - 45$

Factor $5$ out of $- 45$ .

$5 (4 x^{2}) + 5 (- 9)$

Factor $5$ out of $5 (4 x^{2}) + 5 (- 9)$ .

$5 (4 x^{2} - 9)$

Step 2

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

$5 ({(2 x)}^{2} - 9)$

Step 3

Rewrite $9$ as $3^{2}$ .

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

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 $a = 2 x$ and $b = 3$ .

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

Remove unnecessary parentheses.

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