Simplify 2r^4-3r^3+2r^2+11r-5+(r^5+10r^3+6r^2-2r+3)+(-5r^4+r^2+7r-6)

$2 r^{4} - 3 r^{3} + 2 r^{2} + 11 r - 5 + (r^{5} + 10 r^{3} + 6 r^{2} - 2 r + 3) + (- 5 r^{4} + r^{2} + 7 r - 6)$

Step 1

Remove parentheses.

$2 r^{4} - 3 r^{3} + 2 r^{2} + 11 r - 5 + r^{5} + 10 r^{3} + 6 r^{2} - 2 r + 3 - 5 r^{4} + r^{2} + 7 r - 6$

Step 2

Subtract $5 r^{4}$ from $2 r^{4}$ .

$- 3 r^{4} - 3 r^{3} + 2 r^{2} + 11 r - 5 + r^{5} + 10 r^{3} + 6 r^{2} - 2 r + 3 + r^{2} + 7 r - 6$

Step 3

Add $- 3 r^{3}$ and $10 r^{3}$ .

$- 3 r^{4} + 7 r^{3} + 2 r^{2} + 11 r - 5 + r^{5} + 6 r^{2} - 2 r + 3 + r^{2} + 7 r - 6$

Step 4

Add $2 r^{2}$ and $6 r^{2}$ .

$- 3 r^{4} + 7 r^{3} + 8 r^{2} + 11 r - 5 + r^{5} - 2 r + 3 + r^{2} + 7 r - 6$

Step 5

Add $8 r^{2}$ and $r^{2}$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + 11 r - 5 + r^{5} - 2 r + 3 + 7 r - 6$

Step 6

Subtract $2 r$ from $11 r$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + 9 r - 5 + r^{5} + 3 + 7 r - 6$

Step 7

Add $9 r$ and $7 r$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + 16 r - 5 + r^{5} + 3 - 6$

Step 8

Simplify the expression.

Add $- 5$ and $3$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + 16 r + r^{5} - 2 - 6$

Subtract $6$ from $- 2$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + 16 r + r^{5} - 8$

Move $16 r$ .

$- 3 r^{4} + 7 r^{3} + 9 r^{2} + r^{5} + 16 r - 8$

Move $9 r^{2}$ .

$- 3 r^{4} + 7 r^{3} + r^{5} + 9 r^{2} + 16 r - 8$

Move $7 r^{3}$ .

$- 3 r^{4} + r^{5} + 7 r^{3} + 9 r^{2} + 16 r - 8$

Reorder $- 3 r^{4}$ and $r^{5}$ .

$r^{5} - 3 r^{4} + 7 r^{3} + 9 r^{2} + 16 r - 8$