Collecting Like Terms (Cambridge International IGCSE Mathematics)

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**

  • If the coefficient is 1 or -1, then it is conventional not to write the 1

    • The coefficient of x is 1
    • The coefficient of -y s -1

• Each term has a positive or negative sign in front

  • In 2x - 3y the coefficient of x is 2 (positive) and the coefficient of -3y is -3 (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

What is a like term?

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

  • The coefficients can be different

    • For example:
    • 2x and 3x
    • 4x² and 6x²
    • 5xy and -7xy

  • These are not like terms:

    • 2x and 3*y *(different letters)
    • 4x² and 6x⁴ (different powers)
    • 5*xy 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 coefficients

  • 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

Exam Hint Don't leave terms like 1x in your final answer in an exam - always simplify them to just x.

Worked Example Simplify

$8a-5b-6a+4b$

Answer:

Collect the a terms first

$8a-6a=2a$

*Then collect the b *terms Don't forget the minus sign in front of the 5**b

$-5b+4b=-b$

Add together the two answers

$2a+-b$

Simplify the signs

$2a-b$