Find the Product 6pq(3p^2+4q)

$6 p q (3 p^{2} + 4 q)$

Apply the distributive property.

$6 p q (3 p^{2}) + 6 p q (4 q)$

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

Move $p^{2}$ .

$6 (p^{2} p) q \cdot 3 + 6 p q (4 q)$

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

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

$6 (p^{2} p^{1}) q \cdot 3 + 6 p q (4 q)$

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

$6 p^{2 + 1} q \cdot 3 + 6 p q (4 q)$

Add $2$ and $1$ .

$6 p^{3} q \cdot 3 + 6 p q (4 q)$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$6 p^{3} q \cdot 3 + 6 p (q \cdot q) \cdot 4$

Multiply $q$ by $q$ .

$6 p^{3} q \cdot 3 + 6 p q^{2} \cdot 4$

Simplify each term.

Multiply $3$ by $6$ .

$18 p^{3} q + 6 p q^{2} \cdot 4$

Multiply $4$ by $6$ .

$18 p^{3} q + 24 p q^{2}$