Basic Math Examples

$\frac{c^{2} - 16}{4 c - 32} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{c^{2} - 4^{2}}{4 c - 32} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

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 $a = c$ and $b = 4$ .

$\frac{(c + 4) (c - 4)}{4 c - 32} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

Step 2

Factor $4$ out of $4 c - 32$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $4 c$ .

$\frac{(c + 4) (c - 4)}{4 (c) - 32} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

Step 2.2

Factor $4$ out of $- 32$ .

$\frac{(c + 4) (c - 4)}{4 c + 4 \cdot - 8} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

Step 2.3

Factor $4$ out of $4 c + 4 \cdot - 8$ .

$\frac{(c + 4) (c - 4)}{4 (c - 8)} \cdot \frac{c^{2} - 64}{c^{2} + 4 c - 32}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Rewrite $64$ as $8^{2}$ .

$\frac{(c + 4) (c - 4)}{4 (c - 8)} \cdot \frac{c^{2} - 8^{2}}{c^{2} + 4 c - 32}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 8$ .

$\frac{(c + 4) (c - 4)}{4 (c - 8)} \cdot \frac{(c + 8) (c - 8)}{c^{2} + 4 c - 32}$

Step 4

Factor $c^{2} + 4 c - 32$ using the AC method.

Tap for more steps...

Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 32$ and whose sum is $4$ .

$- 4, 8$

Step 4.2

Write the factored form using these integers.

$\frac{(c + 4) (c - 4)}{4 (c - 8)} \cdot \frac{(c + 8) (c - 8)}{(c - 4) (c + 8)}$

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

Cancel the common factor of $c - 4$ .

Tap for more steps...

Step 5.1.1

Factor $c - 4$ out of $(c + 4) (c - 4)$ .

$\frac{(c - 4) (c + 4)}{4 (c - 8)} \cdot \frac{(c + 8) (c - 8)}{(c - 4) (c + 8)}$

Step 5.1.2

Cancel the common factor.

$\frac{(c - 4) (c + 4)}{4 (c - 8)} \cdot \frac{(c + 8) (c - 8)}{(c - 4) (c + 8)}$

Step 5.1.3

Rewrite the expression.

$\frac{c + 4}{4 (c - 8)} \cdot \frac{(c + 8) (c - 8)}{c + 8}$

Step 5.2

Cancel the common factor of $c - 8$ .

Tap for more steps...

Step 5.2.1

Factor $c - 8$ out of $4 (c - 8)$ .

$\frac{c + 4}{(c - 8) \cdot 4} \cdot \frac{(c + 8) (c - 8)}{c + 8}$

Step 5.2.2

Factor $c - 8$ out of $(c + 8) (c - 8)$ .

$\frac{c + 4}{(c - 8) \cdot 4} \cdot \frac{(c - 8) (c + 8)}{c + 8}$

Step 5.2.3

Cancel the common factor.

$\frac{c + 4}{(c - 8) \cdot 4} \cdot \frac{(c - 8) (c + 8)}{c + 8}$

Step 5.2.4

Rewrite the expression.

$\frac{c + 4}{4} \cdot \frac{c + 8}{c + 8}$

Step 5.3

Multiply $\frac{c + 4}{4}$ by $\frac{c + 8}{c + 8}$ .

$\frac{(c + 4) (c + 8)}{4 (c + 8)}$

Step 5.4

Cancel the common factor of $c + 8$ .

Tap for more steps...

Step 5.4.1

Cancel the common factor.

$\frac{(c + 4) (c + 8)}{4 (c + 8)}$

Step 5.4.2

Rewrite the expression.

$\frac{c + 4}{4}$