Simplify (9x+1)(9x-1)

$(9 x + 1) (9 x - 1)$

Step 1

Expand $(9 x + 1) (9 x - 1)$ using the FOIL Method.

Apply the distributive property.

$9 x (9 x - 1) + 1 (9 x - 1)$

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 1 + 1 (9 x - 1)$

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 1 + 1 (9 x) + 1 \cdot - 1$

Step 2

Simplify terms.

Combine the opposite terms in $9 x (9 x) + 9 x \cdot - 1 + 1 (9 x) + 1 \cdot - 1$ .

Reorder the factors in the terms $9 x \cdot - 1$ and $1 (9 x)$ .

$9 x (9 x) - 1 \cdot 9 x + 1 \cdot 9 x + 1 \cdot - 1$

Add $- 1 \cdot 9 x$ and $1 \cdot 9 x$ .

$9 x (9 x) + 0 + 1 \cdot - 1$

Add $9 x (9 x)$ and $0$ .

$9 x (9 x) + 1 \cdot - 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 9 x \cdot x + 1 \cdot - 1$

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

Move $x$ .

$9 \cdot 9 (x \cdot x) + 1 \cdot - 1$

Multiply $x$ by $x$ .

$9 \cdot 9 x^{2} + 1 \cdot - 1$

Multiply $9$ by $9$ .

$81 x^{2} + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$81 x^{2} - 1$