Calculus Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

One to any power is one.

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

Step 2.2

One to any power is one.

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

Step 2.3

Multiply $5$ by $1$ .

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

Step 2.4

One to any power is one.

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

Step 2.5

Multiply $10$ by $1$ .

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

Step 2.6

One to any power is one.

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

Step 2.7

Multiply $10$ by $1$ .

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

Step 2.8

Multiply $5$ by $1$ .

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