Precalculus Examples

$a b^{- 2} (a b^{2} - 3 b^{3})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$a \frac{1}{b^{2}} (a b^{2} - 3 b^{3})$

Step 2

Combine $a$ and $\frac{1}{b^{2}}$ .

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

Step 3

Multiply $\frac{a}{b^{2}}$ by $a b^{2} - 3 b^{3}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Factor $b^{2}$ out of $b^{2} a + b^{2} (- 3 b)$ .

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

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

Step 5

Cancel the common factor of $b^{2}$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $a (a - 3 b)$ by $1$ .

$a (a - 3 b)$

Step 6

Apply the distributive property.

$a \cdot a + a (- 3 b)$

Step 7

Simplify the expression.

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Step 7.1

Multiply $a$ by $a$ .

$a^{2} + a (- 3 b)$

Step 7.2

Rewrite using the commutative property of multiplication.

$a^{2} - 3 a b$