Algebraic Expressions



In this lesson, we will learn what are variables, constants, terms, expressions, and coefficients.

Related Topics: Operations on Algebraic Expressions

Algebraic Terms & Expressions

In mathematics, often the value of a certain number may be unknown. A variable is a symbol, usually a letter, which is used to represent an unknown number.

Some examples of variables are:

x, a, t, y, b

A term can be a number, a variable, or a number and variable combined by multiplication or division.

Some examples of terms are:

x, 8, 4y,


An expression can be term or a collection of terms separated by addition or subtraction operators. Some examples of expressions, with the numbers of terms, are listed below:



Expression

Number of Terms

Description

6x

1

A number multiplied by a variable. The number is always written first followed by the variable(s).

3w – 8

2

Terms separated by –

7b + 5t – 6

3

Terms separated by + and –

1

All multiplication and division, no + or – symbol

Example:

Determine the number of terms in the following expressions:

a) 5xyz

b) 3x + 2y – 2x + 6

Solution:

a) 5xyz has one term

b) 3x + 2y – 2x + 6 has four terms

Coefficients Of Algebraic Terms

The number (positive or negative) in the algebraic term is called the coefficient.

For example:

For the term 4x, 4 is the coefficient

For the term –7y, –7 is the coefficient

The coefficient of 1 in an algebraic term is usually not written.

For example:

1y can be written as simply y. So, 1y and y are the same.

 

Example:

Find the coefficient and variable of each of the following terms:

a) 0.2m

b) –3p

c) q

d) z

e)

Solution:

a) 0.2m (The coefficient is 0.2 and the variable is m)

b) –3p (The coefficient is –3 and the variable is p)

c) q (The coefficient is and the variable is q)

d) z (The coefficient is 1 and the variable is z)

e) (The coefficient is and the variable is x)




Terms of an Algebraic Expression
A presentation of the terms of an algebraic expression. The number and types of terms are presented. Constants, variables and numerical coefficients, terms and expressions are discussed.

This video shows the parts of an expression (terms, coefficients and variables) then explains about evaluating expressions using some examples.






In this video, you'll learn how to identify the parts of an expression in Algebra. You'll learn about expressions, terms, coefficients, and more.



Simplifying Expressions and Combining Like Terms
Expressions are put into their simplest form so as not to be confusing or too complex. One way of simplifying expressions is to combine like terms. By combining terms we can shorten and simplify our expressions, making them easier to read. Like terms often contain the same variable or variables. This video shows how to simplify algebraic expressions by using the distributive property and combine like terms.






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