## Variable Expression

Evaluating Variable Expressions

First off, what is a variable expression?

A variable expression is a combination of mathematical operations (addition, subtraction, multiplication, and division) and terms that contain at least one variable.

Let’s go over some terminology:

Variable: a letter that represents an

unknown amount.

Ex: 4b + 10= 18, b is the variable

Coefficient: the number multiplied by

the variable, found in front of the variable.

Ex: 4b + 10, 4 is the coefficient

Constant: the term that contains only

a number and no variables

Ex: 4b + 10, 10 is the constant

Term: the part of an expression or equation

that is added or subtracted

Ex: 4b + 10= 18, 4b and 10 are the terms

Helpful Tips: Variables and constants are terms. If the variables and constants have multiplication or division symbols in between, they are terms also.

What are the 5 types of variable expressions?

Monomial: is one term and can be a number,

a variable, or the product of a number

and variables with an exponent

Binomial: An expression with two monomials

Trinomial: An expression with three monomials

Polynomial: An expression with one

or more monomials

Multinomial: a mathematical expression

that consists of the sum of several terms

Helpful Tip: Not all multinomials are polynomial, but polynomials can be multinomials. This is because polynomials are limited to positive integer powers of variables. A multinomial can contain square roots of a or other irrational functions of variables.

Let’s evaluate a variable expression together:

6x^2 + 4x+16

x=-3

What kind of expression is this?

Trinomial

Step 1: Substitute x for -2 in the expression.

6(-3)^2+ 4(-3)+16

Step 2: Utilize the order of operations to find the solution.

6(9)-12+16

54-12+16

58