Simplify (-10a^3b^2+25a^2b^5-5a^2b)/(-5a^2b)

$\frac{- 10 a^{3} b^{2} + 25 a^{2} b^{5} - 5 a^{2} b}{- 5 a^{2} b}$

Step 1

Factor $5 a^{2} b$ out of $- 10 a^{3} b^{2} + 25 a^{2} b^{5} - 5 a^{2} b$ .

Factor $5 a^{2} b$ out of $- 10 a^{3} b^{2}$ .

$\frac{5 a^{2} b (- 2 a b) + 25 a^{2} b^{5} - 5 a^{2} b}{- 5 a^{2} b}$

Factor $5 a^{2} b$ out of $25 a^{2} b^{5}$ .

$\frac{5 a^{2} b (- 2 a b) + 5 a^{2} b (5 b^{4}) - 5 a^{2} b}{- 5 a^{2} b}$

Factor $5 a^{2} b$ out of $- 5 a^{2} b$ .

$\frac{5 a^{2} b (- 2 a b) + 5 a^{2} b (5 b^{4}) + 5 a^{2} b (- 1)}{- 5 a^{2} b}$

Factor $5 a^{2} b$ out of $5 a^{2} b (- 2 a b) + 5 a^{2} b (5 b^{4})$ .

$\frac{5 a^{2} b (- 2 a b + 5 b^{4}) + 5 a^{2} b (- 1)}{- 5 a^{2} b}$

Factor $5 a^{2} b$ out of $5 a^{2} b (- 2 a b + 5 b^{4}) + 5 a^{2} b (- 1)$ .

$\frac{5 a^{2} b (- 2 a b + 5 b^{4} - 1)}{- 5 a^{2} b}$

Step 2

Cancel the common factor of $5$ and $- 5$ .

Factor $5$ out of $5 a^{2} b (- 2 a b + 5 b^{4} - 1)$ .

$\frac{5 (a^{2} b (- 2 a b + 5 b^{4} - 1))}{- 5 a^{2} b}$

Cancel the common factors.

Factor $5$ out of $- 5 a^{2} b$ .

$\frac{5 (a^{2} b (- 2 a b + 5 b^{4} - 1))}{5 (- a^{2} b)}$

Cancel the common factor.

$\frac{5 (a^{2} b (- 2 a b + 5 b^{4} - 1))}{5 (- a^{2} b)}$

Rewrite the expression.

$\frac{a^{2} b (- 2 a b + 5 b^{4} - 1)}{- a^{2} b}$

Step 3

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

Cancel the common factor.

$\frac{a^{2} b (- 2 a b + 5 b^{4} - 1)}{- a^{2} b}$

Rewrite the expression.

$\frac{b (- 2 a b + 5 b^{4} - 1)}{- 1 b}$

Step 4

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b (- 2 a b + 5 b^{4} - 1)}{- 1 b}$

Rewrite the expression.

$\frac{- 2 a b + 5 b^{4} - 1}{- 1}$

Move the negative one from the denominator of $\frac{- 2 a b + 5 b^{4} - 1}{- 1}$ .

$- 1 \cdot (- 2 a b + 5 b^{4} - 1)$

Step 5

Rewrite $- 1 \cdot (- 2 a b + 5 b^{4} - 1)$ as $- (- 2 a b + 5 b^{4} - 1)$ .

$- (- 2 a b + 5 b^{4} - 1)$

Step 6

Apply the distributive property.

$- (- 2 a b) - (5 b^{4}) - - 1$

Step 7

Simplify.

Multiply $- 2$ by $- 1$ .

$2 (a b) - (5 b^{4}) - - 1$

Multiply $5$ by $- 1$ .

$2 (a b) - 5 b^{4} - - 1$

Multiply $- 1$ by $- 1$ .

$2 (a b) - 5 b^{4} + 1$

Step 8

Reorder $2 a b$ and $- 5 b^{4}$ .

$- 5 b^{4} + 2 a b + 1$

Simplify (-10a^3b^2+25a^2b^5-5a^2b)/(-5a^2b)

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