Simplify (3ab^2-2)(ab+2)

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

Step 1

Expand $(3 a b^{2} - 2) (a b + 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $b^{2}$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b^{2}$ .

Raise $b$ to the power of $1$ .

$3 a^{2} (b^{1} b^{2}) + 3 a b^{2} \cdot 2 - 2 (a b) - 2 \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 a^{2} b^{1 + 2} + 3 a b^{2} \cdot 2 - 2 (a b) - 2 \cdot 2$

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

$3 a^{2} b^{3} + 6 a b^{2} - 2 (a b) - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$3 a^{2} b^{3} + 6 a b^{2} - 2 a b - 4$