Collecting like terms (Edexcel GCSE Maths): Revision Notes
Collecting like terms
What are expressions, equations and formulae?
In algebra, we use letters to represent unknown numbers. It's important to understand the difference between three key types of mathematical statements:
Expression: A mathematical statement that contains numbers, letters and operations but has no equals sign. For example, 4x + 3y - z. An expression cannot be solved because there's no equals sign to work with.
Equation: A mathematical statement that contains an equals sign with expressions on both sides. For example, 3n - 1 = 17. Equations can be solved to find the value of the unknown letter.
Formula: A special type of equation used to calculate one value when you know other values. For example, A = ½bh is the formula for the area of a triangle. You cannot solve a formula, but you can use it to calculate values.
Understanding like terms
Like terms are terms that contain exactly the same combination of letters raised to the same powers.
When simplifying algebraic expressions, you can only combine terms that are alike. This process is called collecting like terms.
For example:
- xy and -3xy are like terms (both contain xy)
- +10xy and -xy are like terms (both contain xy)
- 3a and +a²bc are NOT like terms (different letter combinations)
- -2ab and -5a²bc are NOT like terms (different powers)
Golden rules for collecting like terms
There are three essential rules you must remember:
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Each term includes its sign: The + or - sign in front of each term belongs to that term and must be included when collecting.
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Don't write the coefficient 1: When you have 'x', this means '1 lot of x'. You don't need to write '1x'.
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Same letters, same powers: Like terms must contain exactly the same combination of letters with identical powers.
How to simplify expressions
To collect like terms and simplify expressions, follow these steps:
- Identify like terms in the expression
- Group like terms together (remember to keep their signs)
- Add or subtract the coefficients of like terms
- Write the simplified expression
Basic examples
When you have the same letter repeated, the process is straightforward:
Basic Example: Repeated Letters
- h + h + h = 3h (three lots of h)
- 5x - 2x = 3x (five lots of x minus two lots of x equals three lots of x)
When you have different types of terms, you need to group carefully:
Example: Mixed Terms
Simplify: 2p + 3q - 5p + q
Step 1: Group like terms: 2p - 5p + 3q + q Step 2: Simplify: -3p + 4q
Worked examples
Worked Example 1: Simplify x + x + x + x
Step 1: Count the x terms: there are 4 lots of x Step 2: Answer: 4x
Worked Example 2: Simplify n³ + n³
Step 1: You have two lots of n³ Step 2: Answer: 2n³
Worked Example 3: Simplify 3m + 6b - 2m + b
Step 1: Group the m terms: 3m - 2m = m Step 2: Group the b terms: 6b + b = 7b Step 3: Answer: m + 7b
Exam tips
Exam Success Tips:
- Practice simplifying algebraic expressions regularly as they appear frequently in GCSE questions
- Remember that n³ + n³ means two lots of n³, which equals 2n³
- When grouping terms, always include the sign that comes before each term
- Take your time to identify like terms correctly before attempting to collect them
- Check your final answer by ensuring all like terms have been properly combined
Remember!
Key Points to Remember:
- Like terms contain exactly the same letters with the same powers
- Always include the sign (+ or -) when collecting terms
- You can only add or subtract like terms, not different types
- Expressions have no equals sign, equations do have an equals sign
- Practice identifying like terms before attempting to collect them