Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite the division as a fraction.

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

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

Factor $n$ out of $8 n$ .

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

Step 1.1.2.3

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

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

Step 1.1.3

Cancel the common factor of $n$ .

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Step 1.1.3.1

Cancel the common factor.

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

Step 1.1.3.2

Rewrite the expression.

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

Step 1.1.3.3

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

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

Step 1.1.4

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

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

Step 1.1.5

Apply the distributive property.

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

Step 1.1.6

Multiply $- 1$ by $8$ .

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

Step 1.2

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

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $8$ by $- 3$ .

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

Step 1.5

Multiply $- 3$ by $- 8$ .

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

Step 2

Add $7$ and $24$ .

$- 24 n^{2} + 31$