Basic Math Examples

$\frac{4 u^{2} - 100}{4^{2} u + 15}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $4 u^{2}$ .

$\frac{4 (u^{2}) - 100}{4^{2} u + 15}$

Step 1.1.2

Factor $4$ out of $- 100$ .

$\frac{4 u^{2} + 4 \cdot - 25}{4^{2} u + 15}$

Step 1.1.3

Factor $4$ out of $4 u^{2} + 4 \cdot - 25$ .

$\frac{4 (u^{2} - 25)}{4^{2} u + 15}$

Step 1.2

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

$\frac{4 (u^{2} - 5^{2})}{4^{2} u + 15}$

Step 1.3

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

$\frac{4 (u + 5) (u - 5)}{4^{2} u + 15}$

Step 2

Raise $4$ to the power of $2$ .

$\frac{4 (u + 5) (u - 5)}{16 u + 15}$