Algebra Examples

$\frac{8}{6 n - 4} \cdot \frac{9 n^{2} - 4}{1}$

Step 1

Factor $2$ out of $6 n - 4$ .

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Step 1.1

Factor $2$ out of $6 n$ .

$\frac{8}{2 (3 n) - 4} \cdot \frac{9 n^{2} - 4}{1}$

Step 1.2

Factor $2$ out of $- 4$ .

$\frac{8}{2 (3 n) + 2 (- 2)} \cdot \frac{9 n^{2} - 4}{1}$

Step 1.3

Factor $2$ out of $2 (3 n) + 2 (- 2)$ .

$\frac{8}{2 (3 n - 2)} \cdot \frac{9 n^{2} - 4}{1}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9 n^{2}$ as ${(3 n)}^{2}$ .

$\frac{8}{2 (3 n - 2)} \cdot \frac{{(3 n)}^{2} - 4}{1}$

Step 2.2

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

$\frac{8}{2 (3 n - 2)} \cdot \frac{{(3 n)}^{2} - 2^{2}}{1}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 n$ and $b = 2$ .

$\frac{8}{2 (3 n - 2)} \cdot \frac{(3 n + 2) (3 n - 2)}{1}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $3 n - 2$ .

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Step 3.1.1

Factor $3 n - 2$ out of $2 (3 n - 2)$ .

$\frac{8}{(3 n - 2) \cdot 2} \cdot \frac{(3 n + 2) (3 n - 2)}{1}$

Step 3.1.2

Factor $3 n - 2$ out of $(3 n + 2) (3 n - 2)$ .

$\frac{8}{(3 n - 2) \cdot 2} \cdot \frac{(3 n - 2) (3 n + 2)}{1}$

Step 3.1.3

Cancel the common factor.

$\frac{8}{(3 n - 2) \cdot 2} \cdot \frac{(3 n - 2) (3 n + 2)}{1}$

Step 3.1.4

Rewrite the expression.

$\frac{8}{2} \cdot (3 n + 2)$

Step 3.2

Divide $8$ by $2$ .

$4 \cdot (3 n + 2)$

Step 3.3

Apply the distributive property.

$4 (3 n) + 4 \cdot 2$

Step 3.4

Multiply.

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Step 3.4.1

Multiply $3$ by $4$ .

$12 n + 4 \cdot 2$

Step 3.4.2

Multiply $4$ by $2$ .

$12 n + 8$