Simplify (11y^3+9xy^3)-(9y^3+8xy^3-2x^4y^3)+(-2y^3+12x^4y^3)

$(11 y^{3} + 9 x y^{3}) - (9 y^{3} + 8 x y^{3} - 2 x^{4} y^{3}) + (- 2 y^{3} + 12 x^{4} y^{3})$

Step 1

Remove parentheses.

$(11 y^{3} + 9 x y^{3}) - (9 y^{3} + 8 x y^{3} - 2 x^{4} y^{3}) - 2 y^{3} + 12 x^{4} y^{3}$

Step 2

Simplify each term.

Apply the distributive property.

$11 y^{3} + 9 x y^{3} - (9 y^{3}) - (8 x y^{3}) - (- 2 x^{4} y^{3}) - 2 y^{3} + 12 x^{4} y^{3}$

Simplify.

Multiply $9$ by $- 1$ .

$11 y^{3} + 9 x y^{3} - 9 y^{3} - (8 x y^{3}) - (- 2 x^{4} y^{3}) - 2 y^{3} + 12 x^{4} y^{3}$

Multiply $8$ by $- 1$ .

$11 y^{3} + 9 x y^{3} - 9 y^{3} - 8 (x y^{3}) - (- 2 x^{4} y^{3}) - 2 y^{3} + 12 x^{4} y^{3}$

Multiply $- 2$ by $- 1$ .

$11 y^{3} + 9 x y^{3} - 9 y^{3} - 8 (x y^{3}) + 2 (x^{4} y^{3}) - 2 y^{3} + 12 x^{4} y^{3}$

Remove parentheses.

$11 y^{3} + 9 x y^{3} - 9 y^{3} - 8 x y^{3} + 2 x^{4} y^{3} - 2 y^{3} + 12 x^{4} y^{3}$

Step 3

Simplify by adding terms.

Subtract $9 y^{3}$ from $11 y^{3}$ .

$2 y^{3} + 9 x y^{3} - 8 x y^{3} + 2 x^{4} y^{3} - 2 y^{3} + 12 x^{4} y^{3}$

Combine the opposite terms in $2 y^{3} + 9 x y^{3} - 8 x y^{3} + 2 x^{4} y^{3} - 2 y^{3} + 12 x^{4} y^{3}$ .

Subtract $2 y^{3}$ from $2 y^{3}$ .

$9 x y^{3} - 8 x y^{3} + 2 x^{4} y^{3} + 0 + 12 x^{4} y^{3}$

Add $9 x y^{3} - 8 x y^{3} + 2 x^{4} y^{3}$ and $0$ .

$9 x y^{3} - 8 x y^{3} + 2 x^{4} y^{3} + 12 x^{4} y^{3}$

Subtract $8 x y^{3}$ from $9 x y^{3}$ .

$1 x y^{3} + 2 x^{4} y^{3} + 12 x^{4} y^{3}$

Multiply $x$ by $1$ .

$x y^{3} + 2 x^{4} y^{3} + 12 x^{4} y^{3}$

Add $2 x^{4} y^{3}$ and $12 x^{4} y^{3}$ .

$x y^{3} + 14 x^{4} y^{3}$