Precalculus Examples

$y = x (4 - x)$

Step 1

Simplify $x (4 - x)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$y = x \cdot 4 + x (- x)$

Step 1.1.2

Reorder.

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Step 1.1.2.1

Move $4$ to the left of $x$ .

$y = 4 \cdot x + x (- x)$

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

$y = 4 \cdot x - x \cdot x$

Step 1.2

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

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Step 1.2.1

Move $x$ .

$y = 4 x - (x \cdot x)$

Step 1.2.2

Multiply $x$ by $x$ .

$y = 4 x - x^{2}$

Step 1.3

Reorder $4 x$ and $- x^{2}$ .

$y = - x^{2} + 4 x$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $2$ .

Not Linear

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