Simplify 7-3((n^3+8n)÷(-n)+9n^2)

$7 - 3 ((n^{3} + 8 n) \div (- n) + 9 n^{2})$

Simplify each term.

Rewrite the division as a fraction.

$7 - 3 (\frac{n^{3} + 8 n}{- n} + 9 n^{2})$

Factor $n$ out of $n^{3} + 8 n$ .

Factor $n$ out of $n^{3}$ .

$7 - 3 (\frac{n \cdot n^{2} + 8 n}{- n} + 9 n^{2})$

Factor $n$ out of $8 n$ .

$7 - 3 (\frac{n \cdot n^{2} + n \cdot 8}{- n} + 9 n^{2})$

Factor $n$ out of $n \cdot n^{2} + n \cdot 8$ .

$7 - 3 (\frac{n (n^{2} + 8)}{- n} + 9 n^{2})$

Cancel the common factor of $n$ .

Cancel the common factor.

$7 - 3 (\frac{n (n^{2} + 8)}{- n} + 9 n^{2})$

Rewrite the expression.

$7 - 3 (\frac{n^{2} + 8}{- 1} + 9 n^{2})$

Move the negative one from the denominator of $\frac{n^{2} + 8}{- 1}$ .

$7 - 3 (- 1 \cdot (n^{2} + 8) + 9 n^{2})$

Rewrite $- 1 \cdot (n^{2} + 8)$ as $- (n^{2} + 8)$ .

$7 - 3 (- (n^{2} + 8) + 9 n^{2})$

Apply the distributive property.

$7 - 3 (- n^{2} - 1 \cdot 8 + 9 n^{2})$

Multiply $- 1$ by $8$ .

$7 - 3 (- n^{2} - 8 + 9 n^{2})$

Add $- n^{2}$ and $9 n^{2}$ .

$7 - 3 (8 n^{2} - 8)$

Apply the distributive property.

$7 - 3 (8 n^{2}) - 3 \cdot - 8$

Multiply $8$ by $- 3$ .

$7 - 24 n^{2} - 3 \cdot - 8$

Multiply $- 3$ by $- 8$ .

$7 - 24 n^{2} + 24$

Add $7$ and $24$ .

$- 24 n^{2} + 31$