Lesson 4: Addition and subtraction of algebraic terms

Objectives

At the end of this lesson, students should be able to:

• Identify or recognise algebraic expressions.

• Know the difference between an algebraic expression and an algebraic equation.

• Know the meaning of coefficients and identify the coefficients of variables.

• Add and subtract algebraic terms.

In algebra, we use letters and symbols to represent numbers. We can use algebra to obtain or display a general formula and hence use this formula to solve problems.

NOTE:

a + 5b – 7c is an algebraic expression.

a + 5b = 7c is an algebraic equation.

a = 7c – 5b is an algebraic formula.

It is important that you clearly understand the difference. An algebraic expression does not have an equality sign (=), but an algebraic equation and an algebraic formula has an equality sign. In an algebraic formula, the coefficient of the variable which is the subject of the formula must be 1. A formula is a general rule which enables the calculation of the value of one variable given the values of the other variables in the formula.

Coefficients

Example 1: What is the coefficient of p in 13p?

Solution: The coefficient of p is 13.

Example 2: What is the coefficient of g in 13p – 4g?

Solution: The coefficient of g is -4.

Addition and subtraction of algebraic terms

You can only add or subtract terms that are the same. These are usually called like terms.                                

Example 3

Simplify 3x + 18x + x + 4x

We add up the coefficients of x in all the terms.

Therefore 3x + 18x + x + 4x = 26x

Example 4

Simplify    m + 6m + 2m² + 3m² + 5m

Solution

We group like terms together.

m+ 6m+ 2m²+3m²+5m = (m+6m+5m) + (2m² + 3m²)

= 12m + 5m² 

NOTE: m and m² are not like terms as a result, you cannot add them together.

Example 5

Simplify   8a – 3b – 2a + 5b

Solution

8a – 3b – 2a + 5b = 8a – 2a+ -3b + 5b

= 6a + 2b

Example 6

Simplify 7y + 7x -2y –y² – 2x

Solution

7y + 7x -2y –y² – 2x = 7y –2y + 7x – 2x– y²

= 5y + 5x – y²