An algebraic equation would contain an equal sign. An algebraic expression would not have an equal sign. An algebraic expression is a phrase made up of one or more algebraic terms. It can include variables, constants, and symbols, such as plus and minus signs. It is important to note that it is an expression and not an equation.

An example of an algebraic expression is

7x2 + 2y

An example of an algebraic equation is

7x2 + 2x = 4

Coefficients are that part of the terms that consist of a number. It is usually the number before the variable. In

7x2 + 2y,

the coefficient of the first term is 7 and the coefficient of the second is 2.

In

7x2 - 3y,

the coefficient of the first term is 7 and the coefficient of the second is -3.

If there is no number before a variable then the coefficient is 1. For example,

x + y = 8.

The coefficient of x is 1 and the coefficient of y is 1 as well.

The constants in an algebraic expression are those terms that just consist of numbers. That is, they are not associated with variables. Constants are those values that cannot be changed.

For example, in the algebraic expression,

7x2 + 6,

the constant is 6.

Let us try these simple statements! Remember, you can use any letter of the alphabet!

The sum of a number and three

x + 3

The product of four and a number

4 × p or 4p

A number taken away from six

b - 6

Eight less a number

h - 8

Five taken away from the product of six and a number

6 × f - 5 or 6f - 5

Let us try some word problems!

A small company has $1000 to give its employees as a bonus. How much money will each employee get?

The algebraic expression to the question is

An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings if he worked for x hours in one day.

$45x - $20

Mary is 13 years old today. If she will be one year older in one year and two years older in two years, how old will she be in x years?

This is very simple to figure out!

Today = 13

Year 1 = 13 + 1

Year 2 = 13 + 2

Year x = 13 + x

Therefore the algebraic expression for the question is

13 + x

We can simplify expressions by grouping like terms

For example,

if we had to add 3v + 6v what would we get?

3v = v + v + v and 6v = v + v + v + v + v + v

3v + 6v = (v + v + v) + (v + v + v + v + v + v)

3v + 6v = 9v

What is 9b - 4b?

9b = b + b + b + b + b + b + b + b + b and 4b = b + b + b + b

9b - 4b =(b + b + b + b + b + b + b + b + b) - (b + b + b + b)

9b - 4b = 5b

What is 7c + 8j - 2c - 6j?

The like terms are 7c and 2c since the both have the same type of variable, c.

The other terms are 8j and 6j since they have the same variable, j.

7c - 2c + 8j - 6j

5c + 2j

NB: 5c cannot be added to 2j because they are not of the same type

Say for example that we knew that a = 4, b = 7, c = 3.

Now if we see an expression which contains any of these letters, all we have to do is replace the letters by their
corresponding numbers to find the value of the expression.

(a) Find the value of 6 + b:

6 + b

Replace b with 7.

6 + 7 = 13.

(b) Find the value of 2a + b:

2a = 2 × a.

(2 × a) + b

Replace a with 4 and b with 7.

(2×4) + 7 = 8 + 7 = 15

(c) Find the value of ab:

ab = a × b

Replace a with 4 and b with 7

4 × 7 = 28.

(d) Find the value of a(b - c):

a(b - c) = a × (b - c).

Replace a with 4, b with 7, and c with 3

4 × (7 - 3) = 16.