Determine if Linear y=4x(8-x)

$y = 4 x (8 - x)$

Step 1

Simplify $4 x (8 - x)$ .

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Multiply $8$ by $4$ .

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

Rewrite using the commutative property of multiplication.

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

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $- 1$ .

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

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

Determine if Linear y=4x(8-x)

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