Calculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(n + 2)}^{2}$ as $(n + 2) (n + 2)$ .

$2 ((n + 2) (n + 2)) - 3 (n + 2) - 2$

Step 1.2

Expand $(n + 2) (n + 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 (n (n + 2) + 2 (n + 2)) - 3 (n + 2) - 2$

Step 1.2.2

Apply the distributive property.

$2 (n \cdot n + n \cdot 2 + 2 (n + 2)) - 3 (n + 2) - 2$

Step 1.2.3

Apply the distributive property.

$2 (n \cdot n + n \cdot 2 + 2 n + 2 \cdot 2) - 3 (n + 2) - 2$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $n$ by $n$ .

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

Step 1.3.1.2

Move $2$ to the left of $n$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

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

Step 1.3.2

Add $2 n$ and $2 n$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify.

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Step 1.5.1

Multiply $4$ by $2$ .

$2 n^{2} + 8 n + 2 \cdot 4 - 3 (n + 2) - 2$

Step 1.5.2

Multiply $2$ by $4$ .

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

Step 1.6

Apply the distributive property.

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

Step 1.7

Multiply $- 3$ by $2$ .

$2 n^{2} + 8 n + 8 - 3 n - 6 - 2$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 n$ from $8 n$ .

$2 n^{2} + 5 n + 8 - 6 - 2$

Step 2.2

Subtract $6$ from $8$ .

$2 n^{2} + 5 n + 2 - 2$

Step 2.3

Combine the opposite terms in $2 n^{2} + 5 n + 2 - 2$ .

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Step 2.3.1

Subtract $2$ from $2$ .

$2 n^{2} + 5 n + 0$

Step 2.3.2

Add $2 n^{2} + 5 n$ and $0$ .

$2 n^{2} + 5 n$