Simplify (a^2-100)/(3a)*(a^2)/(2a-20)

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

Simplify the numerator.

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

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

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 $b = 10$ .

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

Simplify terms.

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

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Factor $2$ out of $2 a$ .

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

Factor $2$ out of $- 20$ .

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

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

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

Cancel the common factor of $a - 10$ .

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Factor $a - 10$ out of $(a + 10) (a - 10)$ .

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

Factor $a - 10$ out of $2 (a - 10)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ .

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Factor $a$ out of $3 a$ .

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

Factor $a$ out of $a^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{a + 10}{3}$ and $\frac{a}{2}$ .

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

Simplify the expression.

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Multiply $3$ by $2$ .

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

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

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

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