Simplify (5x+1)(5x-1)

$(5 x + 1) (5 x - 1)$

Expand $(5 x + 1) (5 x - 1)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x - 1) + 1 (5 x - 1)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 1 + 1 (5 x - 1)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1$

Simplify terms.

Combine the opposite terms in $5 x (5 x) + 5 x \cdot - 1 + 1 (5 x) + 1 \cdot - 1$ .

Reorder the factors in the terms $5 x \cdot - 1$ and $1 (5 x)$ .

$5 x (5 x) - 1 \cdot 5 x + 1 \cdot 5 x + 1 \cdot - 1$

Add $- 1 \cdot 5 x$ and $1 \cdot 5 x$ .

$5 x (5 x) + 0 + 1 \cdot - 1$

Add $5 x (5 x)$ and $0$ .

$5 x (5 x) + 1 \cdot - 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 1 \cdot - 1$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 1 \cdot - 1$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 1 \cdot - 1$

Multiply $5$ by $5$ .

$25 x^{2} + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$25 x^{2} - 1$