Calculus Examples

$(40000 + \frac{10000}{5} x) (30 - x) + (40000 + \frac{10000}{5} x) (5)$

Step 1

Simplify each term.

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Step 1.1

Divide $10000$ by $5$ .

$(40000 + 2000 x) (30 - x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.2

Expand $(40000 + 2000 x) (30 - x)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$40000 (30 - x) + 2000 x (30 - x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.2.2

Apply the distributive property.

$40000 \cdot 30 + 40000 (- x) + 2000 x (30 - x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.2.3

Apply the distributive property.

$40000 \cdot 30 + 40000 (- x) + 2000 x \cdot 30 + 2000 x (- x) + (40000 + \frac{10000}{5} x) (5)$

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 $40000$ by $30$ .

$1200000 + 40000 (- x) + 2000 x \cdot 30 + 2000 x (- x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.2

Multiply $- 1$ by $40000$ .

$1200000 - 40000 x + 2000 x \cdot 30 + 2000 x (- x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.3

Multiply $30$ by $2000$ .

$1200000 - 40000 x + 60000 x + 2000 x (- x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$1200000 - 40000 x + 60000 x + 2000 \cdot - 1 x \cdot x + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.5

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.5.1

Move $x$ .

$1200000 - 40000 x + 60000 x + 2000 \cdot - 1 (x \cdot x) + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.5.2

Multiply $x$ by $x$ .

$1200000 - 40000 x + 60000 x + 2000 \cdot - 1 x^{2} + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.1.6

Multiply $2000$ by $- 1$ .

$1200000 - 40000 x + 60000 x - 2000 x^{2} + (40000 + \frac{10000}{5} x) (5)$

Step 1.3.2

Add $- 40000 x$ and $60000 x$ .

$1200000 + 20000 x - 2000 x^{2} + (40000 + \frac{10000}{5} x) (5)$

Step 1.4

Divide $10000$ by $5$ .

$1200000 + 20000 x - 2000 x^{2} + (40000 + 2000 x) \cdot 5$

Step 1.5

Apply the distributive property.

$1200000 + 20000 x - 2000 x^{2} + 40000 \cdot 5 + 2000 x \cdot 5$

Step 1.6

Multiply $40000$ by $5$ .

$1200000 + 20000 x - 2000 x^{2} + 200000 + 2000 x \cdot 5$

Step 1.7

Multiply $5$ by $2000$ .

$1200000 + 20000 x - 2000 x^{2} + 200000 + 10000 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $1200000$ and $200000$ .

$20000 x - 2000 x^{2} + 1400000 + 10000 x$

Step 2.2

Add $20000 x$ and $10000 x$ .

$30000 x - 2000 x^{2} + 1400000$

Step 2.3

Reorder $30000 x$ and $- 2000 x^{2}$ .

$- 2000 x^{2} + 30000 x + 1400000$