Simplify (x^4+5y^3+6)-(3x^4-2+5xy)-(-y^3+4+6xy)

$(x^{4} + 5 y^{3} + 6) - (3 x^{4} - 2 + 5 x y) - (- y^{3} + 4 + 6 x y)$

Step 1

Simplify each term.

Apply the distributive property.

$x^{4} + 5 y^{3} + 6 - (3 x^{4}) - - 2 - (5 x y) - (- y^{3} + 4 + 6 x y)$

Simplify.

Multiply $3$ by $- 1$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} - - 2 - (5 x y) - (- y^{3} + 4 + 6 x y)$

Multiply $- 1$ by $- 2$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - (5 x y) - (- y^{3} + 4 + 6 x y)$

Multiply $5$ by $- 1$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 (x y) - (- y^{3} + 4 + 6 x y)$

Apply the distributive property.

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y - - y^{3} - 1 \cdot 4 - (6 x y)$

Simplify.

Multiply $- - y^{3}$ .

Multiply $- 1$ by $- 1$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y + 1 y^{3} - 1 \cdot 4 - (6 x y)$

Multiply $y^{3}$ by $1$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y + y^{3} - 1 \cdot 4 - (6 x y)$

Multiply $- 1$ by $4$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y + y^{3} - 4 - (6 x y)$

Multiply $6$ by $- 1$ .

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y + y^{3} - 4 - 6 (x y)$

$x^{4} + 5 y^{3} + 6 - 3 x^{4} + 2 - 5 x y + y^{3} - 4 - 6 x y$

Step 2

Simplify by adding terms.

Subtract $3 x^{4}$ from $x^{4}$ .

$- 2 x^{4} + 5 y^{3} + 6 + 2 - 5 x y + y^{3} - 4 - 6 x y$

Add $5 y^{3}$ and $y^{3}$ .

$- 2 x^{4} + 6 y^{3} + 6 + 2 - 5 x y - 4 - 6 x y$

Simplify by adding and subtracting.

Add $6$ and $2$ .

$- 2 x^{4} + 6 y^{3} + 8 - 5 x y - 4 - 6 x y$

Subtract $4$ from $8$ .

$- 2 x^{4} + 6 y^{3} - 5 x y + 4 - 6 x y$

Subtract $6 x y$ from $- 5 x y$ .

$- 2 x^{4} + 6 y^{3} - 11 x y + 4$