Basic Math Examples

$\frac{9 a^{2} b - 16 b^{3}}{12 a b + 16 b^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $b$ out of $9 a^{2} b - 16 b^{3}$ .

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Step 1.1.1

Factor $b$ out of $9 a^{2} b$ .

$\frac{b (9 a^{2}) - 16 b^{3}}{12 a b + 16 b^{2}}$

Step 1.1.2

Factor $b$ out of $- 16 b^{3}$ .

$\frac{b (9 a^{2}) + b (- 16 b^{2})}{12 a b + 16 b^{2}}$

Step 1.1.3

Factor $b$ out of $b (9 a^{2}) + b (- 16 b^{2})$ .

$\frac{b (9 a^{2} - 16 b^{2})}{12 a b + 16 b^{2}}$

Step 1.2

Rewrite $9 a^{2}$ as ${(3 a)}^{2}$ .

$\frac{b ({(3 a)}^{2} - 16 b^{2})}{12 a b + 16 b^{2}}$

Step 1.3

Rewrite $16 b^{2}$ as ${(4 b)}^{2}$ .

$\frac{b ({(3 a)}^{2} - {(4 b)}^{2})}{12 a b + 16 b^{2}}$

Step 1.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a$ and $b = 4 b$ .

$\frac{b ((3 a + 4 b) (3 a - (4 b)))}{12 a b + 16 b^{2}}$

Step 1.5

Multiply $4$ by $- 1$ .

$\frac{b (3 a + 4 b) (3 a - 4 b)}{12 a b + 16 b^{2}}$

Step 2

Simplify terms.

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Step 2.1

Factor $4 b$ out of $12 a b + 16 b^{2}$ .

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Step 2.1.1

Factor $4 b$ out of $12 a b$ .

$\frac{b (3 a + 4 b) (3 a - 4 b)}{4 b (3 a) + 16 b^{2}}$

Step 2.1.2

Factor $4 b$ out of $16 b^{2}$ .

$\frac{b (3 a + 4 b) (3 a - 4 b)}{4 b (3 a) + 4 b (4 b)}$

Step 2.1.3

Factor $4 b$ out of $4 b (3 a) + 4 b (4 b)$ .

$\frac{b (3 a + 4 b) (3 a - 4 b)}{4 b (3 a + 4 b)}$

Step 2.2

Cancel the common factor of $b$ .

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Step 2.2.1

Cancel the common factor.

$\frac{b (3 a + 4 b) (3 a - 4 b)}{4 b (3 a + 4 b)}$

Step 2.2.2

Rewrite the expression.

$\frac{(3 a + 4 b) (3 a - 4 b)}{4 (3 a + 4 b)}$

Step 2.3

Cancel the common factor of $3 a + 4 b$ .

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Step 2.3.1

Cancel the common factor.

$\frac{(3 a + 4 b) (3 a - 4 b)}{4 (3 a + 4 b)}$

Step 2.3.2

Rewrite the expression.

$\frac{3 a - 4 b}{4}$