Trigonometry Examples

$\frac{a^{2} - 100}{3 a} \cdot \frac{a^{2}}{2 a - 20}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $100$ as $10^{2}$ .

$\frac{a^{2} - 10^{2}}{3 a} \cdot \frac{a^{2}}{2 a - 20}$

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 $b = 10$ .

$\frac{(a + 10) (a - 10)}{3 a} \cdot \frac{a^{2}}{2 a - 20}$

Step 2

Simplify terms.

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Step 2.1

Factor $2$ out of $2 a - 20$ .

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Step 2.1.1

Factor $2$ out of $2 a$ .

$\frac{(a + 10) (a - 10)}{3 a} \cdot \frac{a^{2}}{2 (a) - 20}$

Step 2.1.2

Factor $2$ out of $- 20$ .

$\frac{(a + 10) (a - 10)}{3 a} \cdot \frac{a^{2}}{2 a + 2 \cdot - 10}$

Step 2.1.3

Factor $2$ out of $2 a + 2 \cdot - 10$ .

$\frac{(a + 10) (a - 10)}{3 a} \cdot \frac{a^{2}}{2 (a - 10)}$

Step 2.2

Combine.

$\frac{(a + 10) (a - 10) a^{2}}{3 a (2 (a - 10))}$

Step 2.3

Cancel the common factor of $a - 10$ .

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Step 2.3.1

Cancel the common factor.

$\frac{(a + 10) (a - 10) a^{2}}{3 a (2 (a - 10))}$

Step 2.3.2

Rewrite the expression.

$\frac{(a + 10) a^{2}}{3 a \cdot (2)}$

Step 2.4

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

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Step 2.4.1

Factor $a$ out of $(a + 10) a^{2}$ .

$\frac{a ((a + 10) a)}{3 a \cdot (2)}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $a$ out of $3 a \cdot (2)$ .

$\frac{a ((a + 10) a)}{a (3 \cdot (2))}$

Step 2.4.2.2

Cancel the common factor.

$\frac{a ((a + 10) a)}{a (3 \cdot (2))}$

Step 2.4.2.3

Rewrite the expression.

$\frac{(a + 10) a}{3 \cdot (2)}$

Step 3

Multiply $3$ by $2$ .

$\frac{(a + 10) a}{6}$

Step 4

Reorder factors in $\frac{(a + 10) a}{6}$ .

$\frac{a (a + 10)}{6}$