Algebra Examples

$5 x^{2} - 20 y^{2}$

Step 1

Factor $5$ out of $5 x^{2} - 20 y^{2}$ .

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Step 1.1

Factor $5$ out of $5 x^{2}$ .

$5 (x^{2}) - 20 y^{2}$

Step 1.2

Factor $5$ out of $- 20 y^{2}$ .

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

Step 1.3

Factor $5$ out of $5 (x^{2}) + 5 (- 4 y^{2})$ .

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

Step 2

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

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

Step 3

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

$5 ((x + 2 y) (x - (2 y)))$

Step 4

Factor.

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Step 4.1

Multiply $2$ by $- 1$ .

$5 ((x + 2 y) (x - 2 y))$

Step 4.2

Remove unnecessary parentheses.

$5 (x + 2 y) (x - 2 y)$