Collecting Like Terms (Cambridge (CIE) IGCSE Maths): Revision Note

Collecting like terms

What happens if there is more than one term?

• Terms can be added and subtracted 

  • The numbers in front of the letters are called coefficients

• Each term has a positive or negative sign in front

  • In 2x - 3y  the sign of the x  term is positive and the sign of the y  term is negative

• Subtractions can be thought of as adding a negative 

  • 2x - 3y  is the same as 2x + (-3y)

    • Just like 20 - 30 is the same as 20 + (-30)

• The order of two terms can be swapped, but the signs must move with their terms 

  • 2x - 3y  is the same as -3y + 2x

    • A plus is now needed in front of the 2x

    • Just like 20 - 30 is the same as -30 + 20

• If no number appears in front of a term, then its number is 1

  • x  is the same as 1x

What is a like term?

• Like terms are terms with exactly the same letters and powers

  • The numbers in front can be different

    • For example:

    • 2x  and 3x

    • 4x²  and 6x²

    • 5xy  and -7xy

  • These are not like terms:

    • 2x  and 3y  (different letters)

    • 4x²  and 6x⁴  (different powers)

    • 5xy  and 7xyz  (different letters)

• Remember multiplication can be done in any order

  • xy  and yx  are like terms

    • So are 2xy  and 3yx

How do I collect like terms?

• Collecting like terms means simplifying by adding or subtracting the numbers in front 

  • 2x + 3x  becomes 5x

  • 4y - 10y  becomes -6y

    • A negative sign is needed here

• If there are different types of like terms, collect them separately

  • For 2x + 4y + 5x - 3y 

    • Collecting the x's gives 2x + 5x = 7x

    • Collecting the y's gives 4y - 3y = y

    • The answer is 7x + y