Basic Math Examples

$\frac{25 - n^{2}}{5} \cdot \frac{5 - n}{2}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{5^{2} - n^{2}}{5} \cdot \frac{5 - n}{2}$

Step 1.2

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 $b = n$ .

$\frac{(5 + n) (5 - n)}{5} \cdot \frac{5 - n}{2}$

Step 2

Multiply $\frac{(5 + n) (5 - n)}{5} \cdot \frac{5 - n}{2}$ .

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Step 2.1

Multiply $\frac{(5 + n) (5 - n)}{5}$ by $\frac{5 - n}{2}$ .

$\frac{(5 + n) (5 - n) (5 - n)}{5 \cdot 2}$

Step 2.2

Raise $5 - n$ to the power of $1$ .

$\frac{(5 + n) ({(5 - n)}^{1} (5 - n))}{5 \cdot 2}$

Step 2.3

Raise $5 - n$ to the power of $1$ .

$\frac{(5 + n) ({(5 - n)}^{1} {(5 - n)}^{1})}{5 \cdot 2}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(5 + n) {(5 - n)}^{1 + 1}}{5 \cdot 2}$

Step 2.5

Add $1$ and $1$ .

$\frac{(5 + n) {(5 - n)}^{2}}{5 \cdot 2}$

Step 2.6

Multiply $5$ by $2$ .

$\frac{(5 + n) {(5 - n)}^{2}}{10}$