Calculus Examples

$80 - 5 {(3 + h)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(3 + h)}^{2}$ as $(3 + h) (3 + h)$ .

$80 - 5 ((3 + h) (3 + h))$

Step 1.2

Expand $(3 + h) (3 + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$80 - 5 (3 (3 + h) + h (3 + h))$

Step 1.2.2

Apply the distributive property.

$80 - 5 (3 \cdot 3 + 3 h + h (3 + h))$

Step 1.2.3

Apply the distributive property.

$80 - 5 (3 \cdot 3 + 3 h + h \cdot 3 + h \cdot h)$

$80 - 5 (3 \cdot 3 + 3 h + h \cdot 3 + h \cdot h)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $3$ by $3$ .

$80 - 5 (9 + 3 h + h \cdot 3 + h \cdot h)$

Step 1.3.1.2

Move $3$ to the left of $h$ .

$80 - 5 (9 + 3 h + 3 \cdot h + h \cdot h)$

Step 1.3.1.3

Multiply $h$ by $h$ .

$80 - 5 (9 + 3 h + 3 h + h^{2})$

$80 - 5 (9 + 3 h + 3 h + h^{2})$

Step 1.3.2

Add $3 h$ and $3 h$ .

$80 - 5 (9 + 6 h + h^{2})$

$80 - 5 (9 + 6 h + h^{2})$

Step 1.4

Apply the distributive property.

$80 - 5 \cdot 9 - 5 (6 h) - 5 h^{2}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 5$ by $9$ .

$80 - 45 - 5 (6 h) - 5 h^{2}$

Step 1.5.2

Multiply $6$ by $- 5$ .

$80 - 45 - 30 h - 5 h^{2}$

$80 - 45 - 30 h - 5 h^{2}$

$80 - 45 - 30 h - 5 h^{2}$

Step 2

Subtract $45$ from $80$ .

$35 - 30 h - 5 h^{2}$

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