Basic Math Examples

$16 y^{2} - 100$

Step 1

Factor $4$ out of $16 y^{2} - 100$ .

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Step 1.1

Factor $4$ out of $16 y^{2}$ .

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

Step 1.2

Factor $4$ out of $- 100$ .

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

Step 1.3

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

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

Step 2

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

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

Step 3

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

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

Step 4

Factor.

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Step 4.1

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

$4 ((2 y + 5) (2 y - 5))$

Step 4.2

Remove unnecessary parentheses.

$4 (2 y + 5) (2 y - 5)$