Find the Perfect Square Trinomial (2x+3)(2x-4)

$(2 x + 3) (2 x - 4)$

Expand $(2 x + 3) (2 x - 4)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 4) + 3 (2 x - 4)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 4 + 3 (2 x - 4)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 4 + 3 (2 x) + 3 \cdot - 4$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 4 + 3 (2 x) + 3 \cdot - 4$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 4 + 3 (2 x) + 3 \cdot - 4$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 4$ by $2$ .

$4 x^{2} - 8 x + 3 (2 x) + 3 \cdot - 4$

Multiply $2$ by $3$ .

$4 x^{2} - 8 x + 6 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$4 x^{2} - 8 x + 6 x - 12$

Add $- 8 x$ and $6 x$ .

$4 x^{2} - 2 x - 12$