Algebra Examples

$- 3 a^{2} b + 6 a^{3} b^{2}$

Step 1

Factor $- 3 a^{2} b$ out of $- 3 a^{2} b + 6 a^{3} b^{2}$ .

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Step 1.1

Reorder $- 3 a^{2} b$ and $6 a^{3} b^{2}$ .

$6 a^{3} b^{2} - 3 a^{2} b$

Step 1.2

Factor $- 3 a^{2} b$ out of $6 a^{3} b^{2}$ .

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

Step 1.3

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

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

Step 1.4

Factor $- 3 a^{2} b$ out of $- 3 a^{2} b (- 2 a b) - 3 a^{2} b (1)$ .

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

Step 2

Factor.

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Step 2.1

Factor $- 1$ out of $- 2 a b + 1$ .

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Step 2.1.1

Factor $- 1$ out of $- 2 a b$ .

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

Step 2.1.2

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

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

Step 2.1.3

Factor $- 1$ out of $- (2 a b) - 1 (- 1)$ .

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

Step 2.2

Remove unnecessary parentheses.

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

Step 3

Combine exponents.

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Step 3.1

Factor out negative.

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

Step 3.2

Multiply $- 3$ by $- 1$ .

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

Step 4

Remove unnecessary parentheses.

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