Collecting like terms Revision Notes for AQA GCSE Maths

Collecting like terms

What are expressions, equations and formulae?

In algebra, letters are used to represent unknown numbers. Understanding the difference between expressions, equations and formulae is essential for collecting like terms effectively.

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Understanding these three concepts is fundamental to algebra success. Each serves a different purpose and follows different rules for manipulation.

Expression

An expression is a mathematical statement that contains numbers, letters and operations but does not have an equals sign. The different parts of an expression that are separated by plus (+) or minus (-) signs are called terms.

Example: $4x + 3y - z$

Equation

An equation is a mathematical statement that contains an equals sign. Equations can be solved to find the value of the unknown letter.

Example: $3n - 1 = 17$

Formula

A formula is a mathematical rule that shows the relationship between different quantities. You can use a formula to calculate one value when you know the other values, but you cannot solve a formula.

Example: $A = \frac{1}{2}bh$

Golden rules for collecting like terms

There are three essential rules you must follow when working with algebraic terms:

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These rules are fundamental - memorise them and apply them consistently in all algebraic work.

Rule 1: Include the sign

Each term includes the sign (+ or -) that appears in front of it. When moving terms around, the sign travels with the term.

Rule 2: Invisible coefficient

The letter x means '1 lot of x'. You don't need to write the number 1 in front of a letter - it's understood to be there.

Rule 3: Like terms definition

Like terms contain exactly the same combination of letters with the same powers. Only like terms can be combined together.

Like terms examples: $xy$ , $-3xy$ , $+10xy$ , $-xy$ NOT like terms examples: $3a$ , $2ab$ , $5a^2bc$

Simplifying expressions by collecting like terms

When you simplify expressions, you collect and combine like terms. This means adding or subtracting terms that contain the same letters.

Basic examples

$h + h + h = 3h$ (three lots of h combined)
$5x - 2x = 3x$ (five lots of x minus two lots of x equals three lots of x)

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The key to success is methodically identifying like terms before attempting to combine them. Rushing this step leads to common mistakes.

Step-by-step method

Identify all the like terms in the expression
Group the like terms together
Add or subtract the coefficients (numbers in front of the letters)
Keep the letter part unchanged

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Worked Example 1: Collecting Like Terms

Simplify: $2p + 3q - 5p + q$

Step 1: Identify like terms

p terms: $2p$ and $-5p$
q terms: $3q$ and $q$

Step 2: Collect like terms

p terms: $2p - 5p = -3p$
q terms: $3q + q = 4q$

Answer: -3p + 4q

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Worked Example 2: Simplifying Mixed Terms

Simplify: $3m + 6b - 2m + b$

Step 1: Group like terms together

m terms: $3m - 2m = m$
b terms: $6b + b = 7b$

Answer: m + 7b

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Key Points to Remember:

Like terms contain exactly the same letters - only these can be combined together
Always include the sign (+ or -) when moving terms around
The number 1 doesn't need to be written in front of letters (x means 1x)
Expressions don't have equals signs, equations do have equals signs
Collect terms with the same letters and add or subtract their coefficients

Collecting like terms (AQA GCSE Maths): Revision Notes