Calculus Examples

$10 {(2 + h)}^{2}$

Step 1

Rewrite ${(2 + h)}^{2}$ as $(2 + h) (2 + h)$ .

$10 ((2 + h) (2 + h))$

Step 2

Expand $(2 + h) (2 + h)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$10 (2 (2 + h) + h (2 + h))$

Step 2.2

Apply the distributive property.

$10 (2 \cdot 2 + 2 h + h (2 + h))$

Step 2.3

Apply the distributive property.

$10 (2 \cdot 2 + 2 h + h \cdot 2 + h \cdot h)$

$10 (2 \cdot 2 + 2 h + h \cdot 2 + h \cdot h)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$10 (4 + 2 h + h \cdot 2 + h \cdot h)$

Step 3.1.2

Move $2$ to the left of $h$ .

$10 (4 + 2 h + 2 \cdot h + h \cdot h)$

Step 3.1.3

Multiply $h$ by $h$ .

$10 (4 + 2 h + 2 h + h^{2})$

$10 (4 + 2 h + 2 h + h^{2})$

Step 3.2

Add $2 h$ and $2 h$ .

$10 (4 + 4 h + h^{2})$

$10 (4 + 4 h + h^{2})$

Step 4

Apply the distributive property.

$10 \cdot 4 + 10 (4 h) + 10 h^{2}$

Step 5

Simplify.

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Step 5.1

Multiply $10$ by $4$ .

$40 + 10 (4 h) + 10 h^{2}$

Step 5.2

Multiply $4$ by $10$ .

$40 + 40 h + 10 h^{2}$

$40 + 40 h + 10 h^{2}$

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