Simplify 9r(r+2s-9)

$9 r (r + 2 s - 9)$

Apply the distributive property.

$9 r \cdot r + 9 r (2 s) + 9 r \cdot - 9$

Simplify.

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$9 (r \cdot r) + 9 r (2 s) + 9 r \cdot - 9$

Multiply $r$ by $r$ .

$9 r^{2} + 9 r (2 s) + 9 r \cdot - 9$

Rewrite using the commutative property of multiplication.

$9 r^{2} + 9 \cdot 2 r s + 9 r \cdot - 9$

Multiply $- 9$ by $9$ .

$9 r^{2} + 9 \cdot 2 r s - 81 r$

Multiply $9$ by $2$ .

$9 r^{2} + 18 r s - 81 r$