Find the Product -3n(n^2-2n+8)

$- 3 n (n^{2} - 2 n + 8)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $n^{2}$ .

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

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

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

$- 3 (n^{2} n^{1}) - 3 n (- 2 n) - 3 n \cdot 8$

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

$- 3 n^{2 + 1} - 3 n (- 2 n) - 3 n \cdot 8$

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $8$ by $- 3$ .

$- 3 n^{3} - 3 \cdot - 2 n \cdot n - 24 n$

Step 3

Simplify each term.

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

Move $n$ .

$- 3 n^{3} - 3 \cdot - 2 (n \cdot n) - 24 n$

Multiply $n$ by $n$ .

$- 3 n^{3} - 3 \cdot - 2 n^{2} - 24 n$

Multiply $- 3$ by $- 2$ .

$- 3 n^{3} + 6 n^{2} - 24 n$