Algebraic 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:

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)

Videos

Algebraic expressions -
Professor Edward Burger explains algebraic expressions

The following video will explain more of what is algebra, what are variables, constants, coefficients, terms, and expressions.

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