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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 5$ by $- 1$ .

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

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

Step 2

Simplify by adding terms.

Subtract $2 r^{2} s$ from $9 r^{2} s$ .

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

Subtract $2 r$ from $- 3 r$ .

$7 r^{2} s + 11 s^{2} - 5 r + 5 s^{2}$

Add $11 s^{2}$ and $5 s^{2}$ .

$7 r^{2} s + 16 s^{2} - 5 r$