Pre-Algebra Examples

$- 5 a b^{2} + 17 a b^{3}$

Step 1

Factor $- a b^{2}$ out of $- 5 a b^{2} + 17 a b^{3}$ .

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Step 1.1

Reorder $- 5 a b^{2}$ and $17 a b^{3}$ .

$17 a b^{3} - 5 a b^{2}$

Step 1.2

Factor $- a b^{2}$ out of $17 a b^{3}$ .

$- a b^{2} (- 17 b) - 5 a b^{2}$

Step 1.3

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

$- a b^{2} (- 17 b) - a b^{2} (5)$

Step 1.4

Factor $- a b^{2}$ out of $- a b^{2} (- 17 b) - a b^{2} (5)$ .

$- a b^{2} (- 17 b + 5)$

Step 2

Factor.

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Step 2.1

Factor $- 1$ out of $- 17 b + 5$ .

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Step 2.1.1

Factor $- 1$ out of $- 17 b$ .

$- a b^{2} (- (17 b) + 5)$

Step 2.1.2

Rewrite $5$ as $- 1 (- 5)$ .

$- a b^{2} (- (17 b) - 1 (- 5))$

Step 2.1.3

Factor $- 1$ out of $- (17 b) - 1 (- 5)$ .

$- a b^{2} (- (17 b - 5))$

Step 2.2

Remove unnecessary parentheses.

$- a b^{2} \cdot - 1 (17 b - 5)$

Step 3

Combine exponents.

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Step 3.1

Factor out negative.

$- (a b^{2} \cdot - 1 (17 b - 5))$

Step 3.2

Multiply $- 1$ by $- 1$ .

$1 (a b^{2} (17 b - 5))$

Step 3.3

Multiply $a$ by $1$ .

$a (b^{2} (17 b - 5))$

Step 4

Remove unnecessary parentheses.

$a b^{2} (17 b - 5)$