Pre-Algebra Examples

$\frac{a^{2} b^{2} - a^{4} b}{a b}$

Step 1

Factor $a^{2} b$ out of $a^{2} b^{2} - a^{4} b$ .

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Step 1.1

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

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

Step 1.2

Factor $a^{2} b$ out of $- a^{4} b$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $a^{2}$ and $a$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a$ out of $a b$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $b$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $a (b - a^{2})$ by $1$ .

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

Step 4

Apply the distributive property.

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

Step 5

Rewrite using the commutative property of multiplication.

$a b - a \cdot a^{2}$

Step 6

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 6.1

Move $a^{2}$ .

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

Step 6.2

Multiply $a^{2}$ by $a$ .

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Step 6.2.1

Raise $a$ to the power of $1$ .

$a b - (a^{2} a^{1})$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a b - a^{2 + 1}$

Step 6.3

Add $2$ and $1$ .

$a b - a^{3}$