Simplify (a^3b^2-a^2b+2b)(-ab)^-1

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

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

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

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

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

Move the negative in front of the fraction.

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Cancel the common factor of $a b$ .

Move the leading negative in $- \frac{1}{a b}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $a$ by $1$ .

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

Cancel the common factor of $b$ .

Move the leading negative in $- \frac{1}{a b}$ into the numerator.

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

Factor $b$ out of $2 b$ .

$- a^{3} b^{2} \frac{1}{a b} + a + b \cdot 2 \frac{- 1}{a b}$

Factor $b$ out of $a b$ .

$- a^{3} b^{2} \frac{1}{a b} + a + b \cdot 2 \frac{- 1}{b a}$

Cancel the common factor.

$- a^{3} b^{2} \frac{1}{a b} + a + b \cdot 2 \frac{- 1}{b a}$

Rewrite the expression.

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

Combine $2$ and $\frac{- 1}{a}$ .

$- a^{3} b^{2} \frac{1}{a b} + a + \frac{2 \cdot - 1}{a}$

Multiply $2$ by $- 1$ .

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

Simplify each term.

Cancel the common factor of $a b$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Simplify (a^3b^2-a^2b+2b)(-ab)^-1

Related Questions

Support LCMGCF.com by disabling your adblocker.