Simplify (ab^2+ba^3)-(4a^3b-ab^2-5ab)

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $4$ by $- 1$ .

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

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

Multiply $- 1$ by $- 1$ .

$a b^{2} + b a^{3} - 4 (a^{3} b) + 1 (a b^{2}) - (- 5 a b)$

Multiply $a$ by $1$ .

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

Multiply $- 5$ by $- 1$ .

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

Remove parentheses.

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

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

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

Subtract $4 a^{3} b$ from $b a^{3}$ .

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

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

Subtract $4 a^{3} b$ from $a^{3} b$ .

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