Simplify 2n(n^2+3n+4)

$2 n (n^{2} + 3 n + 4)$

Step 1

Apply the distributive property.

$2 n \cdot n^{2} + 2 n (3 n) + 2 n \cdot 4$

Step 2

Simplify.

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

Move $n^{2}$ .

$2 (n^{2} n) + 2 n (3 n) + 2 n \cdot 4$

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

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

$2 (n^{2} n^{1}) + 2 n (3 n) + 2 n \cdot 4$

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

$2 n^{2 + 1} + 2 n (3 n) + 2 n \cdot 4$

Add $2$ and $1$ .

$2 n^{3} + 2 n (3 n) + 2 n \cdot 4$

Rewrite using the commutative property of multiplication.

$2 n^{3} + 2 \cdot 3 n \cdot n + 2 n \cdot 4$

Multiply $4$ by $2$ .

$2 n^{3} + 2 \cdot 3 n \cdot n + 8 n$

Step 3

Simplify each term.

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$2 n^{3} + 2 \cdot 3 (n \cdot n) + 8 n$

Multiply $n$ by $n$ .

$2 n^{3} + 2 \cdot 3 n^{2} + 8 n$

Multiply $2$ by $3$ .

$2 n^{3} + 6 n^{2} + 8 n$