Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $3$ by $- 1$ .

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

Step 2.2.2

Multiply $- 5$ by $- 1$ .

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

Step 2.3

Remove parentheses.

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

Step 2.4

Apply the distributive property.

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

Step 2.5

Multiply $- 3$ by $- 1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $5 a b$ from $- 3 a b$ .

$- b^{2} + 5 a^{2} b + a^{2} - 8 a b + 2 b^{2} - a^{2} b + 3 a^{2} - b^{2}$

Step 3.2

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

$b^{2} + 5 a^{2} b + a^{2} - 8 a b - a^{2} b + 3 a^{2} - b^{2}$

Step 3.3

Combine the opposite terms in $b^{2} + 5 a^{2} b + a^{2} - 8 a b - a^{2} b + 3 a^{2} - b^{2}$ .

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Step 3.3.1

Subtract $b^{2}$ from $b^{2}$ .

$5 a^{2} b + a^{2} - 8 a b - a^{2} b + 3 a^{2} + 0$

Step 3.3.2

Add $5 a^{2} b + a^{2} - 8 a b - a^{2} b + 3 a^{2}$ and $0$ .

$5 a^{2} b + a^{2} - 8 a b - a^{2} b + 3 a^{2}$

Step 3.4

Subtract $a^{2} b$ from $5 a^{2} b$ .

$a^{2} - 8 a b + 4 a^{2} b + 3 a^{2}$

Step 3.5

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

$4 a^{2} - 8 a b + 4 a^{2} b$