Simplify (ab+3)(3-ab)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Move $3$ to the left of $a b$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $3$ by $3$ .

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

Multiply $- 1$ by $3$ .

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

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

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

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

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