Expand the Trigonometric Expression (7g+3)(-g-3)

$(7 g + 3) (- g - 3)$

Step 1

Expand $(7 g + 3) (- g - 3)$ using the FOIL Method.

Apply the distributive property.

$7 g (- g - 3) + 3 (- g - 3)$

Apply the distributive property.

$7 g (- g) + 7 g \cdot - 3 + 3 (- g - 3)$

Apply the distributive property.

$7 g (- g) + 7 g \cdot - 3 + 3 (- g) + 3 \cdot - 3$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot - 1 g \cdot g + 7 g \cdot - 3 + 3 (- g) + 3 \cdot - 3$

Multiply $g$ by $g$ by adding the exponents.

Move $g$ .

$7 \cdot - 1 (g \cdot g) + 7 g \cdot - 3 + 3 (- g) + 3 \cdot - 3$

Multiply $g$ by $g$ .

$7 \cdot - 1 g^{2} + 7 g \cdot - 3 + 3 (- g) + 3 \cdot - 3$

Multiply $7$ by $- 1$ .

$- 7 g^{2} + 7 g \cdot - 3 + 3 (- g) + 3 \cdot - 3$

Multiply $- 3$ by $7$ .

$- 7 g^{2} - 21 g + 3 (- g) + 3 \cdot - 3$

Multiply $- 1$ by $3$ .

$- 7 g^{2} - 21 g - 3 g + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$- 7 g^{2} - 21 g - 3 g - 9$

Subtract $3 g$ from $- 21 g$ .

$- 7 g^{2} - 24 g - 9$