Calculus Examples

$8 {(x + h)}^{3}$

Step 1

Use the Binomial Theorem.

$8 (x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3})$

Step 2

Apply the distributive property.

$8 x^{3} + 8 (3 x^{2} h) + 8 (3 x h^{2}) + 8 h^{3}$

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $8$ .

$8 x^{3} + 24 (x^{2} h) + 8 (3 x h^{2}) + 8 h^{3}$

Step 3.2

Multiply $3$ by $8$ .

$8 x^{3} + 24 (x^{2} h) + 24 (x h^{2}) + 8 h^{3}$

Step 4

Remove parentheses.

$8 x^{3} + 24 x^{2} h + 24 x h^{2} + 8 h^{3}$

Step 5

Simplify the expression.

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Step 5.1

Move $x^{2}$ .

$8 x^{3} + 24 h x^{2} + 24 x h^{2} + 8 h^{3}$

Step 5.2

Move $x$ .

$8 x^{3} + 24 h x^{2} + 24 h^{2} x + 8 h^{3}$

Step 5.3

Move $8 x^{3}$ .

$24 h x^{2} + 24 h^{2} x + 8 h^{3} + 8 x^{3}$

Step 5.4

Move $24 h x^{2}$ .

$24 h^{2} x + 8 h^{3} + 24 h x^{2} + 8 x^{3}$

Step 5.5

Reorder $24 h^{2} x$ and $8 h^{3}$ .

$8 h^{3} + 24 h^{2} x + 24 h x^{2} + 8 x^{3}$