Factor 9a^2-25b^2

$9 a^{2} - 25 b^{2}$

Step 1

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

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

Step 2

Rewrite $25 b^{2}$ as ${(5 b)}^{2}$ .

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

Step 3

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 $b = 5 b$ .

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

Step 4

Multiply $5$ by $- 1$ .

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

Factor 9a^2-25b^2

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