Algebra Examples

$\frac{a^{2} - 4}{3} \cdot \frac{9}{a + 2}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{a^{2} - 2^{2}}{3} \cdot \frac{9}{a + 2}$

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 $a = a$ and $b = 2$ .

$\frac{(a + 2) (a - 2)}{3} \cdot \frac{9}{a + 2}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a + 2$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(a + 2) (a - 2)}{3} \cdot \frac{9}{a + 2}$

Step 2.1.2

Rewrite the expression.

$\frac{a - 2}{3} \cdot 9$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $9$ .

$\frac{a - 2}{3} \cdot (3 (3))$

Step 2.2.2

Cancel the common factor.

$\frac{a - 2}{3} \cdot (3 \cdot 3)$

Step 2.2.3

Rewrite the expression.

$(a - 2) \cdot 3$

Step 2.3

Apply the distributive property.

$a \cdot 3 - 2 \cdot 3$

Step 2.4

Simplify the expression.

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Step 2.4.1

Move $3$ to the left of $a$ .

$3 \cdot a - 2 \cdot 3$

Step 2.4.2

Multiply $- 2$ by $3$ .

$3 a - 6$