Basic Math Examples

$\frac{a^{2} - 64 b^{2}}{a + 8 b} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $64 b^{2}$ as ${(8 b)}^{2}$ .

$\frac{a^{2} - {(8 b)}^{2}}{a + 8 b} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

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 $b = 8 b$ .

$\frac{(a + 8 b) (a - (8 b))}{a + 8 b} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 1.3

Multiply $8$ by $- 1$ .

$\frac{(a + 8 b) (a - 8 b)}{a + 8 b} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{(a + 8 b) (a - 8 b)}{a + 8 b}$ by cancelling the common factors.

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Step 2.1.1

Cancel the common factor.

$\frac{(a + 8 b) (a - 8 b)}{a + 8 b} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 2.1.2

Rewrite the expression.

$\frac{a - 8 b}{1} \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 2.2

Divide $a - 8 b$ by $1$ .

$(a - 8 b) \div (a + 8 b) \cdot \frac{5 b}{a - 8 b}$

Step 3

Rewrite the division as a fraction.

$\frac{a - 8 b}{a + 8 b} \cdot \frac{5 b}{a - 8 b}$

Step 4

Cancel the common factor of $a - 8 b$ .

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Step 4.1

Cancel the common factor.

$\frac{a - 8 b}{a + 8 b} \cdot \frac{5 b}{a - 8 b}$

Step 4.2

Rewrite the expression.

$\frac{1}{a + 8 b} \cdot (5 b)$

Step 5

Combine $5$ and $\frac{1}{a + 8 b}$ .

$\frac{5}{a + 8 b} \cdot b$

Step 6

Combine $\frac{5}{a + 8 b}$ and $b$ .

$\frac{5 b}{a + 8 b}$