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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Step 2

Simplify by adding terms.

Combine the opposite terms in $- 2 a^{2} b + a^{2} - 5 a b + 3 a b^{2} - b^{2} + 2 a^{2} b + 4 a b$ .

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

$a^{2} - 5 a b + 3 a b^{2} - b^{2} + 0 + 4 a b$

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

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

Add $- 5 a b$ and $4 a b$ .

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

Simplify the expression.

Move $- b^{2}$ .

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

Reorder $a^{2}$ and $3 a b^{2}$ .

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