Simplify 3ab(2a^2+3b^3)

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

Step 1

Apply the distributive property.

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

Step 2

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Multiply $b$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

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

Multiply $b^{3}$ by $b$ .

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

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

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

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

Add $3$ and $1$ .

$3 a^{3} b \cdot 2 + 3 a b^{4} \cdot 3$

Step 4

Simplify each term.

Multiply $2$ by $3$ .

$6 a^{3} b + 3 a b^{4} \cdot 3$

Multiply $3$ by $3$ .

$6 a^{3} b + 9 a b^{4}$