Calculus Examples

$\frac{(10 {(- 5)}^{3} + 10) - (10 {(5)}^{3} + 10)}{5 + 3}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $- 5$ to the power of $3$ .

$\frac{10 \cdot - 125 + 10 - (10 \cdot 5^{3} + 10)}{5 + 3}$

Step 1.2

Multiply $10$ by $- 125$ .

$\frac{- 1250 + 10 - (10 \cdot 5^{3} + 10)}{5 + 3}$

Step 1.3

Simplify each term.

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Step 1.3.1

Raise $5$ to the power of $3$ .

$\frac{- 1250 + 10 - (10 \cdot 125 + 10)}{5 + 3}$

Step 1.3.2

Multiply $10$ by $125$ .

$\frac{- 1250 + 10 - (1250 + 10)}{5 + 3}$

Step 1.4

Add $1250$ and $10$ .

$\frac{- 1250 + 10 - 1 \cdot 1260}{5 + 3}$

Step 1.5

Multiply $- 1$ by $1260$ .

$\frac{- 1250 + 10 - 1260}{5 + 3}$

Step 1.6

Add $- 1250$ and $10$ .

$\frac{- 1240 - 1260}{5 + 3}$

Step 1.7

Subtract $1260$ from $- 1240$ .

$\frac{- 2500}{5 + 3}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Add $5$ and $3$ .

$\frac{- 2500}{8}$

Step 2.2

Cancel the common factor of $- 2500$ and $8$ .

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Step 2.2.1

Factor $4$ out of $- 2500$ .

$\frac{4 (- 625)}{8}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $4$ out of $8$ .

$\frac{4 \cdot - 625}{4 \cdot 2}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 \cdot - 625}{4 \cdot 2}$

Step 2.2.2.3

Rewrite the expression.

$\frac{- 625}{2}$

Step 2.3

Move the negative in front of the fraction.

$- \frac{625}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{625}{2}$

Decimal Form:

$- 312.5$

Mixed Number Form:

$- 312 \frac{1}{2}$