Simplify (12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)

$(12 a^{2} b - 8 a + 5 a^{2} b - 2 a b) - (4 a b^{2} - 6 a b + 2 a + 3 a b)$

Simplify each term.

Add $- 6 a b$ and $3 a b$ .

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (4 a b^{2} + 2 a - 3 a b)$

Apply the distributive property.

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (4 a b^{2}) - (2 a) - (- 3 a b)$

Simplify.

Multiply $4$ by $- 1$ .

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - 4 (a b^{2}) - (2 a) - (- 3 a b)$

Multiply $2$ by $- 1$ .

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - 4 (a b^{2}) - 2 a - (- 3 a b)$

Multiply $- 3$ by $- 1$ .

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - 4 (a b^{2}) - 2 a + 3 (a b)$

Remove parentheses.

$12 a^{2} b - 8 a + 5 a^{2} b - 2 a b - 4 a b^{2} - 2 a + 3 a b$

Simplify by adding terms.

Add $12 a^{2} b$ and $5 a^{2} b$ .

$- 8 a + 17 a^{2} b - 2 a b - 4 a b^{2} - 2 a + 3 a b$

Subtract $2 a$ from $- 8 a$ .

$- 10 a + 17 a^{2} b - 2 a b - 4 a b^{2} + 3 a b$

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

$- 10 a + 17 a^{2} b + 1 a b - 4 a b^{2}$

Multiply $a$ by $1$ .

$- 10 a + 17 a^{2} b + a b - 4 a b^{2}$