Calculus Examples

$2 {(x + h)}^{3}$

Step 1

Use the Binomial Theorem.

$2 (x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3})$

Step 2

Apply the distributive property.

$2 x^{3} + 2 (3 x^{2} h) + 2 (3 x h^{2}) + 2 h^{3}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply $3$ by $2$ .

$2 x^{3} + 6 (x^{2} h) + 2 (3 x h^{2}) + 2 h^{3}$

Step 3.2

Multiply $3$ by $2$ .

$2 x^{3} + 6 (x^{2} h) + 6 (x h^{2}) + 2 h^{3}$

$2 x^{3} + 6 (x^{2} h) + 6 (x h^{2}) + 2 h^{3}$

Step 4

Remove parentheses.

$2 x^{3} + 6 x^{2} h + 6 x h^{2} + 2 h^{3}$

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Move $x^{2}$ .

$2 x^{3} + 6 h x^{2} + 6 x h^{2} + 2 h^{3}$

Step 5.2

Move $x$ .

$2 x^{3} + 6 h x^{2} + 6 h^{2} x + 2 h^{3}$

Step 5.3

Move $2 x^{3}$ .

$6 h x^{2} + 6 h^{2} x + 2 h^{3} + 2 x^{3}$

Step 5.4

Move $6 h x^{2}$ .

$6 h^{2} x + 2 h^{3} + 6 h x^{2} + 2 x^{3}$

Step 5.5

Reorder $6 h^{2} x$ and $2 h^{3}$ .

$2 h^{3} + 6 h^{2} x + 6 h x^{2} + 2 x^{3}$

$2 h^{3} + 6 h^{2} x + 6 h x^{2} + 2 x^{3}$

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