Algebra Examples

$y = 4 x (8 - x)$

Step 1

Simplify $4 x (8 - x)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$y = 4 x \cdot 8 + 4 x (- x)$

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply $8$ by $4$ .

$y = 32 x + 4 x (- x)$

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

$y = 32 x + 4 \cdot - 1 x \cdot x$

Step 1.2

Simplify each term.

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Step 1.2.1

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

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Step 1.2.1.1

Move $x$ .

$y = 32 x + 4 \cdot - 1 (x \cdot x)$

Step 1.2.1.2

Multiply $x$ by $x$ .

$y = 32 x + 4 \cdot - 1 x^{2}$

Step 1.2.2

Multiply $4$ by $- 1$ .

$y = 32 x - 4 x^{2}$

Step 1.3

Reorder $32 x$ and $- 4 x^{2}$ .

$y = - 4 x^{2} + 32 x$

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