Expand the Trigonometric Expression (9+q)(8-q)

$(9 + q) (8 - q)$

Step 1

Expand $(9 + q) (8 - q)$ using the FOIL Method.

Apply the distributive property.

$9 (8 - q) + q (8 - q)$

Apply the distributive property.

$9 \cdot 8 + 9 (- q) + q (8 - q)$

Apply the distributive property.

$9 \cdot 8 + 9 (- q) + q \cdot 8 + q (- q)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $8$ .

$72 + 9 (- q) + q \cdot 8 + q (- q)$

Multiply $- 1$ by $9$ .

$72 - 9 q + q \cdot 8 + q (- q)$

Move $8$ to the left of $q$ .

$72 - 9 q + 8 \cdot q + q (- q)$

Rewrite using the commutative property of multiplication.

$72 - 9 q + 8 q - q \cdot q$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$72 - 9 q + 8 q - (q \cdot q)$

Multiply $q$ by $q$ .

$72 - 9 q + 8 q - q^{2}$

Add $- 9 q$ and $8 q$ .

$72 - q - q^{2}$