Simplify 3n(4n^2+5n)

$3 n (4 n^{2} + 5 n)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$3 n (4 n^{2}) + 3 n (5 n)$

Reorder.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 n \cdot n^{2} + 3 n (5 n)$

Rewrite using the commutative property of multiplication.

$3 \cdot 4 n \cdot n^{2} + 3 \cdot 5 n \cdot n$

Step 2

Simplify each term.

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

Move $n^{2}$ .

$3 \cdot 4 (n^{2} n) + 3 \cdot 5 n \cdot n$

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

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

$3 \cdot 4 (n^{2} n^{1}) + 3 \cdot 5 n \cdot n$

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

$3 \cdot 4 n^{2 + 1} + 3 \cdot 5 n \cdot n$

Add $2$ and $1$ .

$3 \cdot 4 n^{3} + 3 \cdot 5 n \cdot n$

Multiply $3$ by $4$ .

$12 n^{3} + 3 \cdot 5 n \cdot n$

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

Move $n$ .

$12 n^{3} + 3 \cdot 5 (n \cdot n)$

Multiply $n$ by $n$ .

$12 n^{3} + 3 \cdot 5 n^{2}$

Multiply $3$ by $5$ .

$12 n^{3} + 15 n^{2}$