Simplify (2x+1)(2x-1)

$(2 x + 1) (2 x - 1)$

Step 1

Expand $(2 x + 1) (2 x - 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 1) + 1 (2 x - 1)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x - 1)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1$

Step 2

Simplify terms.

Combine the opposite terms in $2 x (2 x) + 2 x \cdot - 1 + 1 (2 x) + 1 \cdot - 1$ .

Reorder the factors in the terms $2 x \cdot - 1$ and $1 (2 x)$ .

$2 x (2 x) - 1 \cdot 2 x + 1 \cdot 2 x + 1 \cdot - 1$

Add $- 1 \cdot 2 x$ and $1 \cdot 2 x$ .

$2 x (2 x) + 0 + 1 \cdot - 1$

Add $2 x (2 x)$ and $0$ .

$2 x (2 x) + 1 \cdot - 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 1 \cdot - 1$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 1 \cdot - 1$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 1 \cdot - 1$

Multiply $2$ by $2$ .

$4 x^{2} + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$4 x^{2} - 1$