Calculus Examples

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

Step 1

Rewrite ${(5 + h)}^{2}$ as $(5 + h) (5 + h)$ .

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

Step 2

Expand $(5 + h) (5 + h)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

$5 \cdot 5 + 5 h + h \cdot 5 + h \cdot h$

$5 \cdot 5 + 5 h + h \cdot 5 + h \cdot h$

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 $5$ by $5$ .

$25 + 5 h + h \cdot 5 + h \cdot h$

Step 3.1.2

Move $5$ to the left of $h$ .

$25 + 5 h + 5 \cdot h + h \cdot h$

Step 3.1.3

Multiply $h$ by $h$ .

$25 + 5 h + 5 h + h^{2}$

$25 + 5 h + 5 h + h^{2}$

Step 3.2

Add $5 h$ and $5 h$ .

$25 + 10 h + h^{2}$

$25 + 10 h + h^{2}$

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