Write in Standard Form -n^2(n^2+5n+6)

$- n^{2} (n^{2} + 5 n + 6)$

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

Apply the distributive property.

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

Step 3

Simplify.

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

Move $n^{2}$ .

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

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

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

Add $2$ and $2$ .

$- n^{4} - n^{2} (5 n) - n^{2} \cdot 6$

Rewrite using the commutative property of multiplication.

$- n^{4} - 1 \cdot 5 n^{2} n - n^{2} \cdot 6$

Multiply $6$ by $- 1$ .

$- n^{4} - 1 \cdot 5 n^{2} n - 6 n^{2}$

Step 4

Simplify each term.

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

Move $n$ .

$- n^{4} - 1 \cdot 5 (n \cdot n^{2}) - 6 n^{2}$

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

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

$- n^{4} - 1 \cdot 5 (n^{1} n^{2}) - 6 n^{2}$

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

$- n^{4} - 1 \cdot 5 n^{1 + 2} - 6 n^{2}$

Add $1$ and $2$ .

$- n^{4} - 1 \cdot 5 n^{3} - 6 n^{2}$

Multiply $- 1$ by $5$ .

$- n^{4} - 5 n^{3} - 6 n^{2}$