Write in Standard Form -3n^2(-2n^3+7n+4n)

$- 3 n^{2} (- 2 n^{3} + 7 n + 4 n)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify terms.

Add $7 n$ and $4 n$ .

$- 3 n^{2} (- 2 n^{3} + 11 n)$

Apply the distributive property.

$- 3 n^{2} (- 2 n^{3}) - 3 n^{2} (11 n)$

Reorder.

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 2 n^{2} n^{3} - 3 n^{2} (11 n)$

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 2 n^{2} n^{3} - 3 \cdot 11 n^{2} n$

Step 3

Simplify each term.

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

Move $n^{3}$ .

$- 3 \cdot - 2 (n^{3} n^{2}) - 3 \cdot 11 n^{2} n$

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

$- 3 \cdot - 2 n^{3 + 2} - 3 \cdot 11 n^{2} n$

Add $3$ and $2$ .

$- 3 \cdot - 2 n^{5} - 3 \cdot 11 n^{2} n$

Multiply $- 3$ by $- 2$ .

$6 n^{5} - 3 \cdot 11 n^{2} n$

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

Move $n$ .

$6 n^{5} - 3 \cdot 11 (n \cdot n^{2})$

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

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

$6 n^{5} - 3 \cdot 11 (n^{1} n^{2})$

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

$6 n^{5} - 3 \cdot 11 n^{1 + 2}$

Add $1$ and $2$ .

$6 n^{5} - 3 \cdot 11 n^{3}$

Multiply $- 3$ by $11$ .

$6 n^{5} - 33 n^{3}$