Simplify (2a^3b^3+10ab^3)-(-14ab^3+9ab^4-12a^3b^3)+(6ab^4-5a^3b^3)

$(2 a^{3} b^{3} + 10 a b^{3}) - (- 14 a b^{3} + 9 a b^{4} - 12 a^{3} b^{3}) + (6 a b^{4} - 5 a^{3} b^{3})$

Step 1

Remove parentheses.

$(2 a^{3} b^{3} + 10 a b^{3}) - (- 14 a b^{3} + 9 a b^{4} - 12 a^{3} b^{3}) + 6 a b^{4} - 5 a^{3} b^{3}$

Step 2

Simplify each term.

Apply the distributive property.

$2 a^{3} b^{3} + 10 a b^{3} - (- 14 a b^{3}) - (9 a b^{4}) - (- 12 a^{3} b^{3}) + 6 a b^{4} - 5 a^{3} b^{3}$

Simplify.

Multiply $- 14$ by $- 1$ .

$2 a^{3} b^{3} + 10 a b^{3} + 14 (a b^{3}) - (9 a b^{4}) - (- 12 a^{3} b^{3}) + 6 a b^{4} - 5 a^{3} b^{3}$

Multiply $9$ by $- 1$ .

$2 a^{3} b^{3} + 10 a b^{3} + 14 (a b^{3}) - 9 (a b^{4}) - (- 12 a^{3} b^{3}) + 6 a b^{4} - 5 a^{3} b^{3}$

Multiply $- 12$ by $- 1$ .

$2 a^{3} b^{3} + 10 a b^{3} + 14 (a b^{3}) - 9 (a b^{4}) + 12 (a^{3} b^{3}) + 6 a b^{4} - 5 a^{3} b^{3}$

Remove parentheses.

$2 a^{3} b^{3} + 10 a b^{3} + 14 a b^{3} - 9 a b^{4} + 12 a^{3} b^{3} + 6 a b^{4} - 5 a^{3} b^{3}$

Step 3

Simplify by adding terms.

Add $2 a^{3} b^{3}$ and $12 a^{3} b^{3}$ .

$14 a^{3} b^{3} + 10 a b^{3} + 14 a b^{3} - 9 a b^{4} + 6 a b^{4} - 5 a^{3} b^{3}$

Subtract $5 a^{3} b^{3}$ from $14 a^{3} b^{3}$ .

$9 a^{3} b^{3} + 10 a b^{3} + 14 a b^{3} - 9 a b^{4} + 6 a b^{4}$

Add $10 a b^{3}$ and $14 a b^{3}$ .

$9 a^{3} b^{3} + 24 a b^{3} - 9 a b^{4} + 6 a b^{4}$

Add $- 9 a b^{4}$ and $6 a b^{4}$ .

$9 a^{3} b^{3} + 24 a b^{3} - 3 a b^{4}$