Expand the Trigonometric Expression (3x-4)(3x+4)

$(3 x - 4) (3 x + 4)$

Expand $(3 x - 4) (3 x + 4)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 4) - 4 (3 x + 4)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 4 - 4 (3 x + 4)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 4 - 4 (3 x) - 4 \cdot 4$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 4 - 4 (3 x) - 4 \cdot 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 4 - 4 (3 x) - 4 \cdot 4$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 4 - 4 (3 x) - 4 \cdot 4$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 4 - 4 (3 x) - 4 \cdot 4$

Multiply $4$ by $3$ .

$9 x^{2} + 12 x - 4 (3 x) - 4 \cdot 4$

Multiply $3$ by $- 4$ .

$9 x^{2} + 12 x - 12 x - 4 \cdot 4$

Multiply $- 4$ by $4$ .

$9 x^{2} + 12 x - 12 x - 16$

Subtract $12 x$ from $12 x$ .

$9 x^{2} + 0 - 16$

Add $9 x^{2}$ and $0$ .

$9 x^{2} - 16$