Expand the Trigonometric Expression (2r-5)(r+10)

$(2 r - 5) (r + 10)$

Expand $(2 r - 5) (r + 10)$ using the FOIL Method.

Apply the distributive property.

$2 r (r + 10) - 5 (r + 10)$

Apply the distributive property.

$2 r \cdot r + 2 r \cdot 10 - 5 (r + 10)$

Apply the distributive property.

$2 r \cdot r + 2 r \cdot 10 - 5 r - 5 \cdot 10$

Simplify and combine like terms.

Simplify each term.

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

Move $r$ .

$2 (r \cdot r) + 2 r \cdot 10 - 5 r - 5 \cdot 10$

Multiply $r$ by $r$ .

$2 r^{2} + 2 r \cdot 10 - 5 r - 5 \cdot 10$

Multiply $10$ by $2$ .

$2 r^{2} + 20 r - 5 r - 5 \cdot 10$

Multiply $- 5$ by $10$ .

$2 r^{2} + 20 r - 5 r - 50$

Subtract $5 r$ from $20 r$ .

$2 r^{2} + 15 r - 50$