We need to distinguish between an expression and a term

So 3x – 2y is an expression with two terms in it. How many terms are in the expression 5x² – 2x + 9 ?

If the “letters part” of a term is the same, we call it a like term. So 3x and 7x are like terms whereas 3x and 7y are not (nor are 3x and 7x²). Because of the commutative law, 2yx and 8xy are also like terms.

Worked Example

• In the lists below, identify any like terms:
  • 4x, 3, -x, 2y, 3xy, 5x
  • 3xy, 4m, -xy, 2, 5yx

Exercise 1

We can write the expression 5x + 4y – 2x, but it is a bit messy. What would be a better way to write it? This process is called collecting like terms.

Worked Example

• Simplify:
  • 9t – 7t + 2t
  • 5a + 2b – 3a + 6b – a – b
  • 2x + 4y – 6 – 5y – x + 3

Whereas expressions are a bit like phrases, equations are like complete sentences, for instance 2x + 1 = 7. They are easy to spot because they always have equals signs in them. We will study them more closely later in the year.

Exercise 2

Answers to both exercises