Evaluate 3x^3(2x+y)

$3 x^{3} (2 x + y)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$3 x^{3} (2 x) + 3 x^{3} y$

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{3} x + 3 x^{3} y$

Step 2

Simplify each term.

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

Move $x$ .

$3 \cdot 2 (x \cdot x^{3}) + 3 x^{3} y$

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

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

$3 \cdot 2 (x^{1} x^{3}) + 3 x^{3} y$

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

$3 \cdot 2 x^{1 + 3} + 3 x^{3} y$

Add $1$ and $3$ .

$3 \cdot 2 x^{4} + 3 x^{3} y$

Multiply $3$ by $2$ .

$6 x^{4} + 3 x^{3} y$