Calculus Examples

$5 {(x + h)}^{2}$

Step 1

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

$5 ((x + h) (x + h))$

Step 2

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

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Step 2.1

Apply the distributive property.

$5 (x (x + h) + h (x + h))$

Step 2.2

Apply the distributive property.

$5 (x \cdot x + x h + h (x + h))$

Step 2.3

Apply the distributive property.

$5 (x \cdot x + x h + h x + h \cdot h)$

$5 (x \cdot x + x h + h x + h \cdot h)$

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 $x$ by $x$ .

$5 (x^{2} + x h + h x + h \cdot h)$

Step 3.1.2

Multiply $h$ by $h$ .

$5 (x^{2} + x h + h x + h^{2})$

$5 (x^{2} + x h + h x + h^{2})$

Step 3.2

Add $x h$ and $h x$ .

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Step 3.2.1

Reorder $x$ and $h$ .

$5 (x^{2} + h x + h x + h^{2})$

Step 3.2.2

Add $h x$ and $h x$ .

$5 (x^{2} + 2 h x + h^{2})$

$5 (x^{2} + 2 h x + h^{2})$

$5 (x^{2} + 2 h x + h^{2})$

Step 4

Apply the distributive property.

$5 x^{2} + 5 (2 h x) + 5 h^{2}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $2$ by $5$ .

$5 x^{2} + 10 (h x) + 5 h^{2}$

Step 5.2

Move $5 x^{2}$ .

$10 h x + 5 h^{2} + 5 x^{2}$

Step 5.3

Reorder $10 h x$ and $5 h^{2}$ .

$5 h^{2} + 10 h x + 5 x^{2}$

$5 h^{2} + 10 h x + 5 x^{2}$

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