Simplify (ab-9)(ab+8)

$(a b - 9) (a b + 8)$

Step 1

Expand $(a b - 9) (a b + 8)$ using the FOIL Method.

Apply the distributive property.

$a b (a b + 8) - 9 (a b + 8)$

Apply the distributive property.

$a b (a b) + a b \cdot 8 - 9 (a b + 8)$

Apply the distributive property.

$a b (a b) + a b \cdot 8 - 9 (a b) - 9 \cdot 8$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

$a \cdot a b \cdot b + a b \cdot 8 - 9 (a b) - 9 \cdot 8$

Multiply $a$ by $a$ .

$a^{2} b \cdot b + a b \cdot 8 - 9 (a b) - 9 \cdot 8$

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

Move $b$ .

$a^{2} (b \cdot b) + a b \cdot 8 - 9 (a b) - 9 \cdot 8$

Multiply $b$ by $b$ .

$a^{2} b^{2} + a b \cdot 8 - 9 (a b) - 9 \cdot 8$

Move $8$ to the left of $a b$ .

$a^{2} b^{2} + 8 \cdot (a b) - 9 (a b) - 9 \cdot 8$

Multiply $- 9$ by $8$ .

$a^{2} b^{2} + 8 a b - 9 a b - 72$

Subtract $9 a b$ from $8 a b$ .

$a^{2} b^{2} - a b - 72$