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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Name

Name	one billion ninety-four million four hundred twenty-five thousand four hundred forty-nine

Interesting facts

1094425449 has 16 divisors, whose sum is 1572076800
The reverse of 1094425449 is 9445244901
Previous prime number is 5569

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	two billion thirty-five million twenty-nine thousand two hundred thirty-five

Interesting facts

2035029235 has 16 divisors, whose sum is 2485956960
The reverse of 2035029235 is 5329205302
Previous prime number is 683

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 31
Digital Root 4

Name

Name	one hundred seventeen million five hundred sixteen thousand nine hundred seventy-nine

Interesting facts

117516979 has 4 divisors, whose sum is 120249976
The reverse of 117516979 is 979615711
Previous prime number is 43

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 46
Digital Root 1

Expand the Logarithmic Expression log base b of ninth root of (x^4)/(y^9x^5)

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