Pre-Algebra Examples

$R (x) = x (26 - \frac{1}{2} x)$

Step 1

Rewrite the function as an equation.

$y = x (26 - \frac{1}{2} x)$

Step 2

Simplify $x (26 - \frac{1}{2} x)$ .

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Step 2.1

Simplify terms.

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Step 2.1.1

Combine $x$ and $\frac{1}{2}$ .

$y = x (26 - \frac{x}{2})$

Step 2.1.2

Apply the distributive property.

$y = x \cdot 26 + x (- \frac{x}{2})$

Step 2.1.3

Reorder.

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Step 2.1.3.1

Move $26$ to the left of $x$ .

$y = 26 \cdot x + x (- \frac{x}{2})$

Step 2.1.3.2

Rewrite using the commutative property of multiplication.

$y = 26 \cdot x - x \frac{x}{2}$

Step 2.2

Multiply $- x \frac{x}{2}$ .

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Step 2.2.1

Combine $\frac{x}{2}$ and $x$ .

$y = 26 x - \frac{x \cdot x}{2}$

Step 2.2.2

Raise $x$ to the power of $1$ .

$y = 26 x - \frac{x^{1} x}{2}$

Step 2.2.3

Raise $x$ to the power of $1$ .

$y = 26 x - \frac{x^{1} x^{1}}{2}$

Step 2.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 26 x - \frac{x^{1 + 1}}{2}$

Step 2.2.5

Add $1$ and $1$ .

$y = 26 x - \frac{x^{2}}{2}$

Step 2.3

Reorder $26 x$ and $- \frac{x^{2}}{2}$ .

$y = - \frac{x^{2}}{2} + 26 x$