Expressions

An expression uses letters to stand for numbers, like 3a + 2b. Like terms have exactly the same letters, so they can be collected: 3a + 5a = 8a. Unlike terms, such as a and b, stay separate.

Key facts

  • 3a means 3 × a; ab means a × b; a² means a × a.
  • Only collect like terms: 2x and 5x, but not 2x and 5x².
  • The sign belongs to the term after it: in 7x − 2y + x, the terms are +7x, −2y, +x.

Worked examples

Example 1

Simplify 5x + 3y − 2x + 4y.

  1. The x terms. 5x − 2x = 3x
  2. The y terms. 3y + 4y = 7y
  3. Put them together. 3x + 7y

Answer: 3x + 7y

Example 2

A rectangle is 2x + 3 long and x wide. Write an expression for its perimeter.

  1. Two lengths and two widths. (2x + 3) + (2x + 3) + x + x
  2. Collect like terms. 6x + 6

Answer: 6x + 6