Find the Product (3ab-c)(3ab+c)

$(3 a b - c) (3 a b + c)$

Expand $(3 a b - c) (3 a b + c)$ using the FOIL Method.

Apply the distributive property.

$3 a b (3 a b + c) - c (3 a b + c)$

Apply the distributive property.

$3 a b (3 a b) + 3 a b c - c (3 a b + c)$

Apply the distributive property.

$3 a b (3 a b) + 3 a b c - c (3 a b) - c \cdot c$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$3 (a \cdot a) b (3 b) + 3 a b c - c (3 a b) - c \cdot c$

Multiply $a$ by $a$ .

$3 a^{2} b (3 b) + 3 a b c - c (3 a b) - c \cdot c$

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

Move $b$ .

$3 a^{2} (b \cdot b) \cdot 3 + 3 a b c - c (3 a b) - c \cdot c$

Multiply $b$ by $b$ .

$3 a^{2} b^{2} \cdot 3 + 3 a b c - c (3 a b) - c \cdot c$

Multiply $3$ by $3$ .

$9 a^{2} b^{2} + 3 a b c - c (3 a b) - c \cdot c$

Multiply $3$ by $- 1$ .

$9 a^{2} b^{2} + 3 a b c - 3 c (a b) - c \cdot c$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$9 a^{2} b^{2} + 3 a b c - 3 c a b - (c \cdot c)$

Multiply $c$ by $c$ .

$9 a^{2} b^{2} + 3 a b c - 3 c a b - c^{2}$

Subtract $3 c a b$ from $3 a b c$ .

Move $c$ .

$9 a^{2} b^{2} + 3 a b c - 3 a b c - c^{2}$

Subtract $3 a b c$ from $3 a b c$ .

$9 a^{2} b^{2} + 0 - c^{2}$

Add $9 a^{2} b^{2}$ and $0$ .

$9 a^{2} b^{2} - c^{2}$