Algebra Examples

$R (x) = 1000 x - x^{2}$ , $C (x) = 3200 + 10 x$

Step 1

Set up the composite result function.

$C (R (x))$

Step 2

Evaluate $C (1000 x - x^{2})$ by substituting in the value of $R$ into $C$ .

$C (1000 x - x^{2}) = 3200 + 10 (1000 x - x^{2})$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$C (1000 x - x^{2}) = 3200 + 10 (1000 x) + 10 (- x^{2})$

Step 3.2

Multiply $1000$ by $10$ .

$C (1000 x - x^{2}) = 3200 + 10000 x + 10 (- x^{2})$

Step 3.3

Multiply $- 1$ by $10$ .

$C (1000 x - x^{2}) = 3200 + 10000 x - 10 x^{2}$

Step 4

Simplify the expression.

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Step 4.1

Move $3200$ .

$C (1000 x - x^{2}) = 10000 x - 10 x^{2} + 3200$

Step 4.2

Reorder $10000 x$ and $- 10 x^{2}$ .

$C (1000 x - x^{2}) = - 10 x^{2} + 10000 x + 3200$