IGCSE Maths / Working with algebra

Collecting like terms revision notes

Edexcel International GCSE Maths (4MA1), chapter 4: Working with algebra, specification point 2.2b-f. Free lesson.

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Collecting like terms means combining terms whose letters and powers match exactly. It helps simplify expressions, while keeping unlike terms separate.

What makes terms alike

Terms are like terms when their letter parts match exactly, including the powers. You can add or subtract the numbers in front, called the coefficients, and leave the letter part unchanged. 3x and 5x are like terms, so 3x + 5x = 8x. 3x and 5y are not like terms because the letters differ. x and x² are not like terms because their powers differ. An x term and an x² term must stay separate.

How to collect terms in an expression

Work with one kind of term at a time. You can rearrange terms to put matching kinds together, but take each term's sign with it when you move it. Then add or subtract the coefficients and bring the results together.

Why x and x² stay separate

It can look as if you should add the numbers in 3x + 4x², but the terms represent different kinds of quantities. For example, if x = 2, then 3x = 6 and 4x² = 16. They cannot be combined by adding their coefficients, so the expression is already in its simplest form. Do not turn 3x + 4x² into 7x². The letter part must match exactly.

A lone letter counts as one

When a letter appears on its own, its coefficient is 1, even though the 1 is not written. So subtracting x means subtracting one x, not zero x. 5x − x = 5x − 1x = 4x.

Check each kind separately

In an expression with both plain letters and powers, collect each matching kind on its own. The final expression can contain several terms if those terms are unlike.