Algebra Examples

$- (2 a b^{2} - a b + b) + 3 a b^{2} - 4 b - (5 a b - a b^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- (2 a b^{2}) - (- a b) - b + 3 a b^{2} - 4 b - (5 a b - a b^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$- 2 (a b^{2}) - (- a b) - b + 3 a b^{2} - 4 b - (5 a b - a b^{2})$

Step 1.2.2

Multiply $- (- a b)$ .

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Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

$- 2 (a b^{2}) + 1 (a b) - b + 3 a b^{2} - 4 b - (5 a b - a b^{2})$

Step 1.2.2.2

Multiply $a$ by $1$ .

$- 2 (a b^{2}) + a b - b + 3 a b^{2} - 4 b - (5 a b - a b^{2})$

Step 1.3

Apply the distributive property.

$- 2 a b^{2} + a b - b + 3 a b^{2} - 4 b - (5 a b) - (- a b^{2})$

Step 1.4

Multiply $5$ by $- 1$ .

$- 2 a b^{2} + a b - b + 3 a b^{2} - 4 b - 5 (a b) - (- a b^{2})$

Step 1.5

Multiply $- (- a b^{2})$ .

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Step 1.5.1

Multiply $- 1$ by $- 1$ .

$- 2 a b^{2} + a b - b + 3 a b^{2} - 4 b - 5 (a b) + 1 (a b^{2})$

Step 1.5.2

Multiply $a$ by $1$ .

$- 2 a b^{2} + a b - b + 3 a b^{2} - 4 b - 5 (a b) + a b^{2}$

$- 2 a b^{2} + a b - b + 3 a b^{2} - 4 b - 5 a b + a b^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 2 a b^{2}$ and $3 a b^{2}$ .

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

Step 2.2

Multiply $a$ by $1$ .

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

Step 2.3

Subtract $5 a b$ from $a b$ .

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

Step 2.4

Subtract $4 b$ from $- b$ .

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

Step 2.5

Add $a b^{2}$ and $a b^{2}$ .

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