Evaluating Variable Expressions

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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.

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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?

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Monomial:  is one term and can be a number,

a variable, or the product of a number

and variables with an exponent

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Binomial: An expression with two monomials

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Trinomial: An expression with three monomials

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Polynomial: An expression with one

or more monomials

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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

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What kind of expression is this? 

Trinomial 

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

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

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

6(9)-12+16

54-12+16

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