Calculus Examples

$15 {(20)}^{2} - \frac{1}{2} \cdot {(20)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Raise $20$ to the power of $2$ .

$15 \cdot 400 - \frac{1}{2} \cdot {(20)}^{3}$

Step 1.2

Multiply $15$ by $400$ .

$6000 - \frac{1}{2} \cdot {(20)}^{3}$

Step 1.3

Raise $20$ to the power of $3$ .

$6000 - \frac{1}{2} \cdot 8000$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$6000 + \frac{- 1}{2} \cdot 8000$

Step 1.4.2

Factor $2$ out of $8000$ .

$6000 + \frac{- 1}{2} \cdot (2 (4000))$

Step 1.4.3

Cancel the common factor.

$6000 + \frac{- 1}{2} \cdot (2 \cdot 4000)$

Step 1.4.4

Rewrite the expression.

$6000 - 1 \cdot 4000$

Step 1.5

Multiply $- 1$ by $4000$ .

$6000 - 4000$

Step 2

Subtract $4000$ from $6000$ .

$2000$