Algebra Examples

$\frac{(n + 2)!}{n!}$

Step 1

Rewrite $(n + 2)!$ as $(n + 2) (n + 1) \cdot n!$ .

$\frac{(n + 2) (n + 1) \cdot n!}{n!}$

Step 2

Cancel the common factor of $n!$ .

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Step 2.1

Cancel the common factor.

$\frac{(n + 2) (n + 1) \cdot n!}{n!}$

Step 2.2

Divide $(n + 2) (n + 1)$ by $1$ .

$(n + 2) (n + 1)$

$(n + 2) (n + 1)$

Step 3

Expand $(n + 2) (n + 1)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$n (n + 1) + 2 (n + 1)$

Step 3.2

Apply the distributive property.

$n \cdot n + n \cdot 1 + 2 (n + 1)$

Step 3.3

Apply the distributive property.

$n \cdot n + n \cdot 1 + 2 n + 2 \cdot 1$

$n \cdot n + n \cdot 1 + 2 n + 2 \cdot 1$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $n$ by $n$ .

$n^{2} + n \cdot 1 + 2 n + 2 \cdot 1$

Step 4.1.2

Multiply $n$ by $1$ .

$n^{2} + n + 2 n + 2 \cdot 1$

Step 4.1.3

Multiply $2$ by $1$ .

$n^{2} + n + 2 n + 2$

$n^{2} + n + 2 n + 2$

Step 4.2

Add $n$ and $2 n$ .

$n^{2} + 3 n + 2$

$n^{2} + 3 n + 2$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$