Calculus Examples

$4 {(x + h)}^{3}$

Step 1

Use the Binomial Theorem.

$4 (x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3})$

Step 2

Apply the distributive property.

$4 x^{3} + 4 (3 x^{2} h) + 4 (3 x h^{2}) + 4 h^{3}$

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $4$ .

$4 x^{3} + 12 (x^{2} h) + 4 (3 x h^{2}) + 4 h^{3}$

Step 3.2

Multiply $3$ by $4$ .

$4 x^{3} + 12 (x^{2} h) + 12 (x h^{2}) + 4 h^{3}$

Step 4

Remove parentheses.

$4 x^{3} + 12 x^{2} h + 12 x h^{2} + 4 h^{3}$

Step 5

Simplify the expression.

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Step 5.1

Move $x^{2}$ .

$4 x^{3} + 12 h x^{2} + 12 x h^{2} + 4 h^{3}$

Step 5.2

Move $x$ .

$4 x^{3} + 12 h x^{2} + 12 h^{2} x + 4 h^{3}$

Step 5.3

Move $4 x^{3}$ .

$12 h x^{2} + 12 h^{2} x + 4 h^{3} + 4 x^{3}$

Step 5.4

Move $12 h x^{2}$ .

$12 h^{2} x + 4 h^{3} + 12 h x^{2} + 4 x^{3}$

Step 5.5

Reorder $12 h^{2} x$ and $4 h^{3}$ .

$4 h^{3} + 12 h^{2} x + 12 h x^{2} + 4 x^{3}$