Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

Multiply $3$ by $- 1$ .

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

Step 1.2.2

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

Tap for more steps...

Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.2.2

Multiply $a^{2}$ by $1$ .

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

Step 1.2.3

Multiply $- 3$ by $- 1$ .

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

Step 1.3

Remove parentheses.

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

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $4 a^{3} b^{2} - a^{2} b^{2} + 2 a b - 3 a^{2} b^{3} + a^{2} b^{2} + 3 a b$ .

Tap for more steps...

Step 2.1.1

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

$4 a^{3} b^{2} + 2 a b - 3 a^{2} b^{3} + 0 + 3 a b$

Step 2.1.2

Add $4 a^{3} b^{2} + 2 a b - 3 a^{2} b^{3}$ and $0$ .

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

Step 2.2

Add $2 a b$ and $3 a b$ .

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