Finite Math Examples

$y = - 3 {(x - 5)}^{2} - 2$

Step 1

Simplify $- 3 {(x - 5)}^{2} - 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$y = - 3 ((x - 5) (x - 5)) - 2$

Step 1.1.2

Expand $(x - 5) (x - 5)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$y = - 3 (x (x - 5) - 5 (x - 5)) - 2$

Step 1.1.2.2

Apply the distributive property.

$y = - 3 (x \cdot x + x \cdot - 5 - 5 (x - 5)) - 2$

Step 1.1.2.3

Apply the distributive property.

$y = - 3 (x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5) - 2$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

$y = - 3 (x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5) - 2$

Step 1.1.3.1.2

Move $- 5$ to the left of $x$ .

$y = - 3 (x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5) - 2$

Step 1.1.3.1.3

Multiply $- 5$ by $- 5$ .

$y = - 3 (x^{2} - 5 x - 5 x + 25) - 2$

Step 1.1.3.2

Subtract $5 x$ from $- 5 x$ .

$y = - 3 (x^{2} - 10 x + 25) - 2$

Step 1.1.4

Apply the distributive property.

$y = - 3 x^{2} - 3 (- 10 x) - 3 \cdot 25 - 2$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $- 10$ by $- 3$ .

$y = - 3 x^{2} + 30 x - 3 \cdot 25 - 2$

Step 1.1.5.2

Multiply $- 3$ by $25$ .

$y = - 3 x^{2} + 30 x - 75 - 2$

Step 1.2

Subtract $2$ from $- 75$ .

$y = - 3 x^{2} + 30 x - 77$

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