Basic Math Examples

$- 25 + 4 y^{2}$

Step 1

Factor $- 1$ out of $- 25 + 4 y^{2}$ .

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Step 1.1

Reorder $- 25$ and $4 y^{2}$ .

$4 y^{2} - 25$

Step 1.2

Factor $- 1$ out of $4 y^{2}$ .

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

Step 1.3

Rewrite $- 25$ as $- 1 (25)$ .

$- (- 4 y^{2}) - 1 (25)$

Step 1.4

Factor $- 1$ out of $- (- 4 y^{2}) - 1 (25)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Reorder $- {(2 y)}^{2}$ and $5^{2}$ .

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

Step 5

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

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

Step 6

Factor.

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Step 6.1

Multiply $2$ by $- 1$ .

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

Step 6.2

Remove unnecessary parentheses.

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