Factor 81x^2-225y^2

$81 x^{2} - 225 y^{2}$

Step 1

Factor $9$ out of $81 x^{2} - 225 y^{2}$ .

Factor $9$ out of $81 x^{2}$ .

$9 (9 x^{2}) - 225 y^{2}$

Factor $9$ out of $- 225 y^{2}$ .

$9 (9 x^{2}) + 9 (- 25 y^{2})$

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

$9 (9 x^{2} - 25 y^{2})$

Step 2

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

$9 ({(3 x)}^{2} - 25 y^{2})$

Step 3

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

$9 ({(3 x)}^{2} - {(5 y)}^{2})$

Step 4

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

$9 ((3 x + 5 y) (3 x - (5 y)))$

Step 5

Factor.

Multiply $5$ by $- 1$ .

$9 ((3 x + 5 y) (3 x - 5 y))$

Remove unnecessary parentheses.

$9 (3 x + 5 y) (3 x - 5 y)$

Factor 81x^2-225y^2

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