Collecting-Like-Terms Aqa Foundation

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Exam code:8300

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

Examiner Tips and Tricks

Don’t leave terms like 1x in your final answer in an exam – always simplify them to just x.

Worked Example

Simplify

$8 a minus 5 b minus 6 a plus 4 b$

Collect the a terms first

$8 a minus 6 a equals 2 a$

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

$negative 5 b plus 4 b equals negative b$

Add together the two answers

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Maths Gcse Aqa Foundation

Collecting-Like-Terms Aqa Foundation