Simplify (6r+2+8r^3)-(5r^3-11-8r^5)-(6r+9r^5)

$(6 r + 2 + 8 r^{3}) - (5 r^{3} - 11 - 8 r^{5}) - (6 r + 9 r^{5})$

Simplify each term.

Apply the distributive property.

$6 r + 2 + 8 r^{3} - (5 r^{3}) - - 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Simplify.

Multiply $5$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} - - 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Multiply $- 1$ by $- 11$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Multiply $- 8$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - (6 r + 9 r^{5})$

Apply the distributive property.

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - (6 r) - (9 r^{5})$

Multiply $6$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - (9 r^{5})$

Multiply $9$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - 9 r^{5}$

Simplify by adding terms.

Combine the opposite terms in $6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - 9 r^{5}$ .

Subtract $6 r$ from $6 r$ .

$2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} + 0 - 9 r^{5}$

Add $2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5}$ and $0$ .

$2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 9 r^{5}$

Add $2$ and $11$ .

$8 r^{3} - 5 r^{3} + 13 + 8 r^{5} - 9 r^{5}$

Subtract $5 r^{3}$ from $8 r^{3}$ .

$3 r^{3} + 13 + 8 r^{5} - 9 r^{5}$

Subtract $9 r^{5}$ from $8 r^{5}$ .

$3 r^{3} + 13 - r^{5}$

Simplify the expression.

Move $13$ .

$3 r^{3} - r^{5} + 13$

Reorder $3 r^{3}$ and $- r^{5}$ .

$- r^{5} + 3 r^{3} + 13$