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Maths Gcse Wjec-Eduqas Higher

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Higher
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  48. Completing-The-Square Wjec-Eduqas Higher
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  51. Algebraic-Roots-And-Indices Wjec-Eduqas Higher
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  52. Introduction-To-Algebra Wjec-Eduqas Higher
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  56. Fractions-Decimals-And-Percentages Wjec-Eduqas Higher
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  58. Percentages Wjec-Eduqas Higher
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  59. Fractions Wjec-Eduqas Higher
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  60. Powers-Roots-And-Standard-Form Wjec-Eduqas Higher
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  61. Prime-Factors-Hcf-And-Lcm- Wjec-Eduqas Higher
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Exam code:C300

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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