Algebra Examples

$\frac{8 n^{2}}{m^{2} - 16} \cdot \frac{m^{2} - 4 m}{6 n}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{8 n^{2}}{m^{2} - 4^{2}} \cdot \frac{m^{2} - 4 m}{6 n}$

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 $a = m$ and $b = 4$ .

$\frac{8 n^{2}}{(m + 4) (m - 4)} \cdot \frac{m^{2} - 4 m}{6 n}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $m$ out of $m^{2} - 4 m$ .

Tap for more steps...

Step 2.1.1

Factor $m$ out of $m^{2}$ .

$\frac{8 n^{2}}{(m + 4) (m - 4)} \cdot \frac{m \cdot m - 4 m}{6 n}$

Step 2.1.2

Factor $m$ out of $- 4 m$ .

$\frac{8 n^{2}}{(m + 4) (m - 4)} \cdot \frac{m \cdot m + m \cdot - 4}{6 n}$

Step 2.1.3

Factor $m$ out of $m \cdot m + m \cdot - 4$ .

$\frac{8 n^{2}}{(m + 4) (m - 4)} \cdot \frac{m (m - 4)}{6 n}$

Step 2.2

Combine.

$\frac{8 n^{2} (m (m - 4))}{(m + 4) (m - 4) (6 n)}$

Step 2.3

Cancel the common factor of $8$ and $6$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $8 n^{2} (m (m - 4))$ .

$\frac{2 (4 n^{2} (m (m - 4)))}{(m + 4) (m - 4) (6 n)}$

Step 2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.2.1

Factor $2$ out of $(m + 4) (m - 4) (6 n)$ .

$\frac{2 (4 n^{2} (m (m - 4)))}{2 ((m + 4) (m - 4) (3 n))}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 (4 n^{2} (m (m - 4)))}{2 ((m + 4) (m - 4) (3 n))}$

Step 2.3.2.3

Rewrite the expression.

$\frac{4 n^{2} (m (m - 4))}{(m + 4) (m - 4) (3 n)}$

Step 2.4

Cancel the common factor of $n^{2}$ and $n$ .

Tap for more steps...

Step 2.4.1

Factor $n$ out of $4 n^{2} (m (m - 4))$ .

$\frac{n (4 n (m (m - 4)))}{(m + 4) (m - 4) (3 n)}$

Step 2.4.2

Cancel the common factors.

Tap for more steps...

Step 2.4.2.1

Factor $n$ out of $(m + 4) (m - 4) (3 n)$ .

$\frac{n (4 n (m (m - 4)))}{n ((m + 4) (m - 4) \cdot (3))}$

Step 2.4.2.2

Cancel the common factor.

$\frac{n (4 n (m (m - 4)))}{n ((m + 4) (m - 4) \cdot (3))}$

Step 2.4.2.3

Rewrite the expression.

$\frac{4 n (m (m - 4))}{(m + 4) (m - 4) \cdot (3)}$

Step 2.5

Cancel the common factor of $m - 4$ .

Tap for more steps...

Step 2.5.1

Cancel the common factor.

$\frac{4 n (m (m - 4))}{(m + 4) (m - 4) \cdot 3}$

Step 2.5.2

Rewrite the expression.

$\frac{4 n (m)}{(m + 4) \cdot (3)}$

Step 2.6

Move $3$ to the left of $m + 4$ .

$\frac{4 n m}{3 (m + 4)}$