Basic Math Examples

$\frac{4 c^{2} - 100}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 1

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

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Step 1.1

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

$\frac{4 (c^{2}) - 100}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 1.2

Factor $4$ out of $- 100$ .

$\frac{4 c^{2} + 4 \cdot - 25}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 1.3

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

$\frac{4 (c^{2} - 25)}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 2

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

$\frac{4 (c^{2} - 5^{2})}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 3

Factor.

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Step 3.1

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 $b = 5$ .

$\frac{4 ((c + 5) (c - 5))}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 3.2

Remove unnecessary parentheses.

$\frac{4 (c + 5) (c - 5)}{16 c^{2} - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 4

Factor $16$ out of $16 c^{2} - 16$ .

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Step 4.1

Factor $16$ out of $16 c^{2}$ .

$\frac{4 (c + 5) (c - 5)}{16 (c^{2}) - 16} \cdot \frac{64 c + 64}{4 c - 20}$

Step 4.2

Factor $16$ out of $- 16$ .

$\frac{4 (c + 5) (c - 5)}{16 (c^{2}) + 16 (- 1)} \cdot \frac{64 c + 64}{4 c - 20}$

Step 4.3

Factor $16$ out of $16 (c^{2}) + 16 (- 1)$ .

$\frac{4 (c + 5) (c - 5)}{16 (c^{2} - 1)} \cdot \frac{64 c + 64}{4 c - 20}$

Step 5

Rewrite $1$ as $1^{2}$ .

$\frac{4 (c + 5) (c - 5)}{16 (c^{2} - 1^{2})} \cdot \frac{64 c + 64}{4 c - 20}$

Step 6

Factor.

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Step 6.1

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 $b = 1$ .

$\frac{4 (c + 5) (c - 5)}{16 ((c + 1) (c - 1))} \cdot \frac{64 c + 64}{4 c - 20}$

Step 6.2

Remove unnecessary parentheses.

$\frac{4 (c + 5) (c - 5)}{16 (c + 1) (c - 1)} \cdot \frac{64 c + 64}{4 c - 20}$

Step 7

Reduce the expression $\frac{4 (c + 5) (c - 5)}{16 (c + 1) (c - 1)}$ by cancelling the common factors.

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Step 7.1

Factor $4$ out of $4 (c + 5) (c - 5)$ .

$\frac{4 ((c + 5) (c - 5))}{16 (c + 1) (c - 1)} \cdot \frac{64 c + 64}{4 c - 20}$

Step 7.2

Factor $4$ out of $16 (c + 1) (c - 1)$ .

$\frac{4 ((c + 5) (c - 5))}{4 (4 (c + 1) (c - 1))} \cdot \frac{64 c + 64}{4 c - 20}$

Step 7.3

Cancel the common factor.

$\frac{4 ((c + 5) (c - 5))}{4 (4 (c + 1) (c - 1))} \cdot \frac{64 c + 64}{4 c - 20}$

Step 7.4

Rewrite the expression.

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 c + 64}{4 c - 20}$

Step 8

Factor $64$ out of $64 c + 64$ .

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Step 8.1

Factor $64$ out of $64 c$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c) + 64}{4 c - 20}$

Step 8.2

Factor $64$ out of $64$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c) + 64 (1)}{4 c - 20}$

Step 8.3

Factor $64$ out of $64 (c) + 64 (1)$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c + 1)}{4 c - 20}$

Step 9

Factor $4$ out of $4 c - 20$ .

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Step 9.1

Factor $4$ out of $4 c$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c + 1)}{4 (c) - 20}$

Step 9.2

Factor $4$ out of $- 20$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c + 1)}{4 c + 4 \cdot - 5}$

Step 9.3

Factor $4$ out of $4 c + 4 \cdot - 5$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{64 (c + 1)}{4 (c - 5)}$

Step 10

Reduce the expression $\frac{64 (c + 1)}{4 (c - 5)}$ by cancelling the common factors.

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Step 10.1

Factor $4$ out of $64 (c + 1)$ .

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{4 (16 (c + 1))}{4 (c - 5)}$

Step 10.2

Cancel the common factor.

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{4 (16 (c + 1))}{4 (c - 5)}$

Step 10.3

Rewrite the expression.

$\frac{(c + 5) (c - 5)}{4 (c + 1) (c - 1)} \cdot \frac{16 (c + 1)}{c - 5}$