Factor 80g^2-45

$80 g^{2} - 45$

Step 1

Factor $5$ out of $80 g^{2} - 45$ .

Factor $5$ out of $80 g^{2}$ .

$5 (16 g^{2}) - 45$

Factor $5$ out of $- 45$ .

$5 (16 g^{2}) + 5 (- 9)$

Factor $5$ out of $5 (16 g^{2}) + 5 (- 9)$ .

$5 (16 g^{2} - 9)$

Step 2

Rewrite $16 g^{2}$ as ${(4 g)}^{2}$ .

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

Step 3

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

$5 ({(4 g)}^{2} - 3^{2})$

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 $a = 4 g$ and $b = 3$ .

$5 ((4 g + 3) (4 g - 3))$

Remove unnecessary parentheses.

$5 (4 g + 3) (4 g - 3)$