Simplify (2x-4)(2x+4)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $4$ by $2$ .

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

Multiply $2$ by $- 4$ .

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

Multiply $- 4$ by $4$ .

$4 x^{2} + 8 x - 8 x - 16$

Subtract $8 x$ from $8 x$ .

$4 x^{2} + 0 - 16$

Add $4 x^{2}$ and $0$ .

$4 x^{2} - 16$