Basic Math Examples

${(n + 1)}^{5}$

Step 1

Use the Binomial Theorem.

$n^{5} + 5 n^{4} \cdot 1 + 10 n^{3} \cdot 1^{2} + 10 n^{2} \cdot 1^{3} + 5 n \cdot 1^{4} + 1^{5}$

Step 2

Simplify each term.

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Step 2.1

Multiply $5$ by $1$ .

$n^{5} + 5 n^{4} + 10 n^{3} \cdot 1^{2} + 10 n^{2} \cdot 1^{3} + 5 n \cdot 1^{4} + 1^{5}$

Step 2.2

One to any power is one.

$n^{5} + 5 n^{4} + 10 n^{3} \cdot 1 + 10 n^{2} \cdot 1^{3} + 5 n \cdot 1^{4} + 1^{5}$

Step 2.3

Multiply $10$ by $1$ .

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} \cdot 1^{3} + 5 n \cdot 1^{4} + 1^{5}$

Step 2.4

One to any power is one.

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} \cdot 1 + 5 n \cdot 1^{4} + 1^{5}$

Step 2.5

Multiply $10$ by $1$ .

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n \cdot 1^{4} + 1^{5}$

Step 2.6

One to any power is one.

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n \cdot 1 + 1^{5}$

Step 2.7

Multiply $5$ by $1$ .

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n + 1^{5}$

Step 2.8

One to any power is one.

$n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n + 1$