Simplify (10a^2b-8a+5a^2b-2ab)-(ab^2-6ab-2a+3ab)

$(10 a^{2} b - 8 a + 5 a^{2} b - 2 a b) - (a b^{2} - 6 a b - 2 a + 3 a b)$

Step 1

Simplify each term.

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

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (a b^{2} - 2 a - 3 a b)$

Apply the distributive property.

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - (a b^{2}) - (- 2 a) - (- 3 a b)$

Simplify.

Multiply $- 2$ by $- 1$ .

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a - (- 3 a b)$

Multiply $- 3$ by $- 1$ .

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a + 3 (a b)$

$10 a^{2} b - 8 a + 5 a^{2} b - 2 a b - a b^{2} + 2 a + 3 a b$

Step 2

Simplify by adding terms.

Add $10 a^{2} b$ and $5 a^{2} b$ .

$- 8 a + 15 a^{2} b - 2 a b - a b^{2} + 2 a + 3 a b$

Add $- 8 a$ and $2 a$ .

$- 6 a + 15 a^{2} b - 2 a b - a b^{2} + 3 a b$

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

$- 6 a + 15 a^{2} b + 1 a b - a b^{2}$

Multiply $a$ by $1$ .

$- 6 a + 15 a^{2} b + a b - a b^{2}$