Find the Product 3a^3(8a+b)

$3 a^{3} (8 a + b)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$3 a^{3} (8 a) + 3 a^{3} b$

Rewrite using the commutative property of multiplication.

$3 \cdot 8 a^{3} a + 3 a^{3} b$

Step 2

Simplify each term.

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

Move $a$ .

$3 \cdot 8 (a \cdot a^{3}) + 3 a^{3} b$

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

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

$3 \cdot 8 (a^{1} a^{3}) + 3 a^{3} b$

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

$3 \cdot 8 a^{1 + 3} + 3 a^{3} b$

Add $1$ and $3$ .

$3 \cdot 8 a^{4} + 3 a^{3} b$

Multiply $3$ by $8$ .

$24 a^{4} + 3 a^{3} b$