Precalculus Examples

$R (x) = 1100 x - x^{2}$ , $C (x) = 3100 + 30 x$

Step 1

Set up the composite result function.

$R (C (x))$

Step 2

Evaluate $R (3100 + 30 x)$ by substituting in the value of $C$ into $R$ .

$R (3100 + 30 x) = 1100 (3100 + 30 x) - {(3100 + 30 x)}^{2}$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$R (3100 + 30 x) = 1100 \cdot 3100 + 1100 (30 x) - {(3100 + 30 x)}^{2}$

Step 3.2

Multiply $1100$ by $3100$ .

$R (3100 + 30 x) = 3410000 + 1100 (30 x) - {(3100 + 30 x)}^{2}$

Step 3.3

Multiply $30$ by $1100$ .

$R (3100 + 30 x) = 3410000 + 33000 x - {(3100 + 30 x)}^{2}$

Step 3.4

Rewrite ${(3100 + 30 x)}^{2}$ as $(3100 + 30 x) (3100 + 30 x)$ .

$R (3100 + 30 x) = 3410000 + 33000 x - ((3100 + 30 x) (3100 + 30 x))$

Step 3.5

Expand $(3100 + 30 x) (3100 + 30 x)$ using the FOIL Method.

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Step 3.5.1

Apply the distributive property.

$R (3100 + 30 x) = 3410000 + 33000 x - (3100 (3100 + 30 x) + 30 x (3100 + 30 x))$

Step 3.5.2

Apply the distributive property.

$R (3100 + 30 x) = 3410000 + 33000 x - (3100 \cdot 3100 + 3100 (30 x) + 30 x (3100 + 30 x))$

Step 3.5.3

Apply the distributive property.

$R (3100 + 30 x) = 3410000 + 33000 x - (3100 \cdot 3100 + 3100 (30 x) + 30 x \cdot 3100 + 30 x (30 x))$

Step 3.6

Simplify and combine like terms.

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Step 3.6.1

Simplify each term.

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Step 3.6.1.1

Multiply $3100$ by $3100$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 3100 (30 x) + 30 x \cdot 3100 + 30 x (30 x))$

Step 3.6.1.2

Multiply $30$ by $3100$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 30 x \cdot 3100 + 30 x (30 x))$

Step 3.6.1.3

Multiply $3100$ by $30$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 93000 x + 30 x (30 x))$

Step 3.6.1.4

Rewrite using the commutative property of multiplication.

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 93000 x + 30 \cdot (30 x \cdot x))$

Step 3.6.1.5

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

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Step 3.6.1.5.1

Move $x$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 93000 x + 30 \cdot (30 (x \cdot x)))$

Step 3.6.1.5.2

Multiply $x$ by $x$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 93000 x + 30 \cdot (30 x^{2}))$

Step 3.6.1.6

Multiply $30$ by $30$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 93000 x + 93000 x + 900 x^{2})$

Step 3.6.2

Add $93000 x$ and $93000 x$ .

$R (3100 + 30 x) = 3410000 + 33000 x - (9610000 + 186000 x + 900 x^{2})$

Step 3.7

Apply the distributive property.

$R (3100 + 30 x) = 3410000 + 33000 x - 1 \cdot 9610000 - (186000 x) - (900 x^{2})$

Step 3.8

Simplify.

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Step 3.8.1

Multiply $- 1$ by $9610000$ .

$R (3100 + 30 x) = 3410000 + 33000 x - 9610000 - (186000 x) - (900 x^{2})$

Step 3.8.2

Multiply $186000$ by $- 1$ .

$R (3100 + 30 x) = 3410000 + 33000 x - 9610000 - 186000 x - (900 x^{2})$

Step 3.8.3

Multiply $900$ by $- 1$ .

$R (3100 + 30 x) = 3410000 + 33000 x - 9610000 - 186000 x - 900 x^{2}$

Step 4

Simplify by adding terms.

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Step 4.1

Subtract $9610000$ from $3410000$ .

$R (3100 + 30 x) = 33000 x - 6200000 - 186000 x - 900 x^{2}$

Step 4.2

Subtract $186000 x$ from $33000 x$ .

$R (3100 + 30 x) = - 153000 x - 6200000 - 900 x^{2}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Move $- 6200000$ .

$R (3100 + 30 x) = - 153000 x - 900 x^{2} - 6200000$

Step 4.3.2

Reorder $- 153000 x$ and $- 900 x^{2}$ .

$R (3100 + 30 x) = - 900 x^{2} - 153000 x - 6200000$