Simplify (3x-1)(3x+1)

$(3 x - 1) (3 x + 1)$

Step 1

Expand $(3 x - 1) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 1) - 1 (3 x + 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 1 - 1 (3 x + 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 1 - 1 (3 x) - 1 \cdot 1$

Step 2

Simplify terms.

Combine the opposite terms in $3 x (3 x) + 3 x \cdot 1 - 1 (3 x) - 1 \cdot 1$ .

Reorder the factors in the terms $3 x \cdot 1$ and $- 1 (3 x)$ .

$3 x (3 x) + 1 \cdot 3 x - 1 \cdot 3 x - 1 \cdot 1$

Subtract $3 x$ from $1 \cdot 3 x$ .

$3 x (3 x) + 0 - 1 \cdot 1$

Add $3 x (3 x)$ and $0$ .

$3 x (3 x) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x - 1 \cdot 1$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) - 1 \cdot 1$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} - 1 \cdot 1$

Multiply $3$ by $3$ .

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

Multiply $- 1$ by $1$ .

$9 x^{2} - 1$