Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Factor $a b$ out of $a b (b) + a b (- a)$ .

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

Step 2

Cancel the common factor of $a b$ .

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Step 2.1

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

$\frac{a b (b - a)}{a b} \cdot \frac{a b (a b)}{a - b}$

Step 2.2

Cancel the common factor.

$\frac{a b (b - a)}{a b} \cdot \frac{a b (a b)}{a - b}$

Step 2.3

Rewrite the expression.

$a b (b - a) \cdot \frac{a b}{a - b}$

Step 3

Combine $a$ and $\frac{a b}{a - b}$ .

$b (b - a) \cdot \frac{a (a b)}{a - b}$

Step 4

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

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

Step 5

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

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

Step 6

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

$b (b - a) \cdot \frac{a^{1 + 1} b}{a - b}$

Step 7

Add $1$ and $1$ .

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

Step 8

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

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

Step 9

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

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

Step 10

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

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

Step 11

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

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

Step 12

Add $1$ and $1$ .

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

Step 13

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

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

Step 14

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

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Step 14.1

Factor $- 1$ out of $b$ .

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

Step 14.2

Factor $- 1$ out of $- a$ .

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

Step 14.3

Factor $- 1$ out of $- 1 (- b) - (a)$ .

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

Step 14.4

Reorder terms.

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

Step 14.5

Cancel the common factor.

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

Step 14.6

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

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

Step 15

Simplify the expression.

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Step 15.1

Move $- 1$ to the left of $a^{2} b^{2}$ .

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

Step 15.2

Rewrite $- 1 (a^{2} b^{2})$ as $- (a^{2} b^{2})$ .

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