Expand the Trigonometric Expression (9b-1)(9b+1)

$(9 b - 1) (9 b + 1)$

Step 1

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

Apply the distributive property.

$9 b (9 b + 1) - 1 (9 b + 1)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

Subtract $9 b$ from $1 \cdot 9 b$ .

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

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

$9 b (9 b) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 9 b \cdot b - 1 \cdot 1$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$9 \cdot 9 (b \cdot b) - 1 \cdot 1$

Multiply $b$ by $b$ .

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

Multiply $9$ by $9$ .

$81 b^{2} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$81 b^{2} - 1$