Algebra Examples

$36 x^{2} - 100 y^{2}$

Step 1

Factor $4$ out of $36 x^{2} - 100 y^{2}$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $36 x^{2}$ .

$4 (9 x^{2}) - 100 y^{2}$

Step 1.2

Factor $4$ out of $- 100 y^{2}$ .

$4 (9 x^{2}) + 4 (- 25 y^{2})$

Step 1.3

Factor $4$ out of $4 (9 x^{2}) + 4 (- 25 y^{2})$ .

$4 (9 x^{2} - 25 y^{2})$

Step 2

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

$4 ({(3 x)}^{2} - 25 y^{2})$

Step 3

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

$4 ({(3 x)}^{2} - {(5 y)}^{2})$

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 $b = 5 y$ .

$4 ((3 x + 5 y) (3 x - (5 y)))$

Step 5

Factor.

Tap for more steps...

Step 5.1

Multiply $5$ by $- 1$ .

$4 ((3 x + 5 y) (3 x - 5 y))$

Step 5.2

Remove unnecessary parentheses.

$4 (3 x + 5 y) (3 x - 5 y)$