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Operations on Algebraic Expressions
In these lessons, we will learn what variables, constants, terms, expressions and coefficients are in algebra.
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) 3
x + 2
y – 2
x + 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.
Parts of an expression and how to evaluate expressions
This video shows the parts of an expression (terms, coefficients and variables) then explains about evaluating expressions using some examples.
What is a Term?
A term is any coefficient and its variable.
Identify the term in the expression:
4x  2y + 5
Identify the coefficient and variable in the term:
7xy
Examples:
1. If x = 4 and y = 2
Evaluate 3x + 5y
2. Evaluate the expression if a = 7 and b = 2
(3 + a)  2b
3. Jim and Jane like to go running in the morning. Jim runs twice as far as Jane. Let J be the distance Jane runs. What is expression for the combined distance they travel?
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.
Examples:
1. Simplify 5x  8 + 3(2x  5)
2. Simplify 5y
^{2}  y  (3y
^{2}  6y) + 8y
3. Simplify 9x
^{3} + 5  [5(x
^{3}  3) + 12]
Algebraic Expression, Terms, and Coefficients
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.
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