Simplify (4x-1)(4x+1)

$(4 x - 1) (4 x + 1)$

Step 1

Expand $(4 x - 1) (4 x + 1)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x + 1) - 1 (4 x + 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 1 - 1 (4 x + 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 1 - 1 (4 x) - 1 \cdot 1$

Step 2

Simplify terms.

Combine the opposite terms in $4 x (4 x) + 4 x \cdot 1 - 1 (4 x) - 1 \cdot 1$ .

Reorder the factors in the terms $4 x \cdot 1$ and $- 1 (4 x)$ .

$4 x (4 x) + 1 \cdot 4 x - 1 \cdot 4 x - 1 \cdot 1$

Subtract $4 x$ from $1 \cdot 4 x$ .

$4 x (4 x) + 0 - 1 \cdot 1$

Add $4 x (4 x)$ and $0$ .

$4 x (4 x) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x - 1 \cdot 1$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) - 1 \cdot 1$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$16 x^{2} - 1$