Calculus Examples

$(62.4 p (- 1200 \cdot 60^{2} + 33.3 \cdot 60^{3} - \frac{60^{4}}{4})) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1

Simplify each term.

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $- 1200 \cdot 60^{2}$ as a fraction with denominator $1$ .

$62.4 p (\frac{- 1200 \cdot 60^{2}}{1} + 33.3 \cdot 60^{3} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.1.2

Multiply $\frac{- 1200 \cdot 60^{2}}{1}$ by $\frac{4}{4}$ .

$62.4 p (\frac{- 1200 \cdot 60^{2}}{1} \cdot \frac{4}{4} + 33.3 \cdot 60^{3} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.1.3

Multiply $\frac{- 1200 \cdot 60^{2}}{1}$ by $\frac{4}{4}$ .

$62.4 p (\frac{- 1200 \cdot 60^{2} \cdot 4}{4} + 33.3 \cdot 60^{3} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.1.4

Write $33.3 \cdot 60^{3}$ as a fraction with denominator $1$ .

$62.4 p (\frac{- 1200 \cdot 60^{2} \cdot 4}{4} + \frac{33.3 \cdot 60^{3}}{1} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.1.5

Multiply $\frac{33.3 \cdot 60^{3}}{1}$ by $\frac{4}{4}$ .

$62.4 p (\frac{- 1200 \cdot 60^{2} \cdot 4}{4} + \frac{33.3 \cdot 60^{3}}{1} \cdot \frac{4}{4} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.1.6

Multiply $\frac{33.3 \cdot 60^{3}}{1}$ by $\frac{4}{4}$ .

$62.4 p (\frac{- 1200 \cdot 60^{2} \cdot 4}{4} + \frac{33.3 \cdot 60^{3} \cdot 4}{4} - \frac{60^{4}}{4}) - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.2

Combine the numerators over the common denominator.

$62.4 p \frac{- 1200 \cdot 60^{2} \cdot 4 + 33.3 \cdot 60^{3} \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3

Simplify each term.

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Step 1.3.1

Raise $60$ to the power of $2$ .

$62.4 p \frac{- 1200 \cdot 3600 \cdot 4 + 33.3 \cdot 60^{3} \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.2

Multiply $- 1200 \cdot 3600 \cdot 4$ .

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Step 1.3.2.1

Multiply $- 1200$ by $3600$ .

$62.4 p \frac{- 4320000 \cdot 4 + 33.3 \cdot 60^{3} \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.2.2

Multiply $- 4320000$ by $4$ .

$62.4 p \frac{- 17280000 + 33.3 \cdot 60^{3} \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.3

Raise $60$ to the power of $3$ .

$62.4 p \frac{- 17280000 + 33.3 \cdot 216000 \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.4

Multiply $33.3 \cdot 216000 \cdot 4$ .

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Step 1.3.4.1

Multiply $33.3$ by $216000$ .

$62.4 p \frac{- 17280000 + 7192800 \cdot 4 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.4.2

Multiply $7192800$ by $4$ .

$62.4 p \frac{- 17280000 + 28771200 - 60^{4}}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.5

Raise $60$ to the power of $4$ .

$62.4 p \frac{- 17280000 + 28771200 - 1 \cdot 12960000}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.3.6

Multiply $- 1$ by $12960000$ .

$62.4 p \frac{- 17280000 + 28771200 - 12960000}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.4

Add $- 17280000$ and $28771200$ .

$62.4 p \frac{11491200 - 12960000}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.5

Subtract $12960000$ from $11491200$ .

$62.4 p \frac{- 1468800}{4} - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.6

Divide $- 1468800$ by $4$ .

$62.4 p \cdot - 367200 - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.7

Multiply $- 367200$ by $62.4$ .

$- 22913280 p - (62.4 p (- 1200 \cdot 40^{2} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.8

Find the common denominator.

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Step 1.8.1

Write $- 1200 \cdot 40^{2}$ as a fraction with denominator $1$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2}}{1} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.8.2

Multiply $\frac{- 1200 \cdot 40^{2}}{1}$ by $\frac{4}{4}$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2}}{1} \cdot \frac{4}{4} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.8.3

Multiply $\frac{- 1200 \cdot 40^{2}}{1}$ by $\frac{4}{4}$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2} \cdot 4}{4} + 33.3 \cdot 40^{3} - \frac{40^{4}}{4}))$

Step 1.8.4

Write $33.3 \cdot 40^{3}$ as a fraction with denominator $1$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2} \cdot 4}{4} + \frac{33.3 \cdot 40^{3}}{1} - \frac{40^{4}}{4}))$

Step 1.8.5

Multiply $\frac{33.3 \cdot 40^{3}}{1}$ by $\frac{4}{4}$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2} \cdot 4}{4} + \frac{33.3 \cdot 40^{3}}{1} \cdot \frac{4}{4} - \frac{40^{4}}{4}))$

Step 1.8.6

Multiply $\frac{33.3 \cdot 40^{3}}{1}$ by $\frac{4}{4}$ .

$- 22913280 p - (62.4 p (\frac{- 1200 \cdot 40^{2} \cdot 4}{4} + \frac{33.3 \cdot 40^{3} \cdot 4}{4} - \frac{40^{4}}{4}))$

Step 1.9

Combine the numerators over the common denominator.

$- 22913280 p - (62.4 p \frac{- 1200 \cdot 40^{2} \cdot 4 + 33.3 \cdot 40^{3} \cdot 4 - 40^{4}}{4})$

Step 1.10

Simplify each term.

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Step 1.10.1

Raise $40$ to the power of $2$ .

$- 22913280 p - (62.4 p \frac{- 1200 \cdot 1600 \cdot 4 + 33.3 \cdot 40^{3} \cdot 4 - 40^{4}}{4})$

Step 1.10.2

Multiply $- 1200 \cdot 1600 \cdot 4$ .

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Step 1.10.2.1

Multiply $- 1200$ by $1600$ .

$- 22913280 p - (62.4 p \frac{- 1920000 \cdot 4 + 33.3 \cdot 40^{3} \cdot 4 - 40^{4}}{4})$

Step 1.10.2.2

Multiply $- 1920000$ by $4$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 33.3 \cdot 40^{3} \cdot 4 - 40^{4}}{4})$

Step 1.10.3

Raise $40$ to the power of $3$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 33.3 \cdot 64000 \cdot 4 - 40^{4}}{4})$

Step 1.10.4

Multiply $33.3 \cdot 64000 \cdot 4$ .

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Step 1.10.4.1

Multiply $33.3$ by $64000$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 2131200 \cdot 4 - 40^{4}}{4})$

Step 1.10.4.2

Multiply $2131200$ by $4$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 8524800 - 40^{4}}{4})$

Step 1.10.5

Raise $40$ to the power of $4$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 8524800 - 1 \cdot 2560000}{4})$

Step 1.10.6

Multiply $- 1$ by $2560000$ .

$- 22913280 p - (62.4 p \frac{- 7680000 + 8524800 - 2560000}{4})$

Step 1.11

Add $- 7680000$ and $8524800$ .

$- 22913280 p - (62.4 p \frac{844800 - 2560000}{4})$

Step 1.12

Subtract $2560000$ from $844800$ .

$- 22913280 p - (62.4 p \frac{- 1715200}{4})$

Step 1.13

Divide $- 1715200$ by $4$ .

$- 22913280 p - (62.4 p \cdot - 428800)$

Step 1.14

Multiply $- 428800$ by $62.4$ .

$- 22913280 p - (- 26757120 p)$

Step 1.15

Multiply $- 26757120$ by $- 1$ .

$- 22913280 p + 26757120 p$

Step 2

Add $- 22913280 p$ and $26757120 p$ .

$3843840 p$