Factor 3a^2-75

$3 a^{2} - 75$

Step 1

Factor $3$ out of $3 a^{2} - 75$ .

Factor $3$ out of $3 a^{2}$ .

$3 (a^{2}) - 75$

Factor $3$ out of $- 75$ .

$3 a^{2} + 3 \cdot - 25$

Factor $3$ out of $3 a^{2} + 3 \cdot - 25$ .

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

Step 2

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

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

Step 3

Factor.

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

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

Remove unnecessary parentheses.

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