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Collecting Like Terms

FoundationHigherAQAEdexcelOCR

Practise collecting like terms with this free Foundation and Higher GCSE Maths worksheet from Virtus Academy. You'll work through simplifying expressions by collecting like terms, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Only terms with exactly the same letters and powers can be combined.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Collecting like terms simplifies an expression by combining terms that contain exactly the same letters raised to the same powers.

So \(3x\) and \(5x\) are like terms and combine to \(8x\), but \(3x\) and \(3y\) are not, and neither are \(3x\) and \(3x^2\). The letter and its power must both match.

The sign in front of a term belongs to it. In \(7a - 3b + 2a\), the terms are \(+7a\), \(-3b\) and \(+2a\), so the \(a\) terms give \(9a\) and the answer is \(9a - 3b\). Losing a sign when rearranging is the most frequent error.

Revision notes

Identifying like terms

Terms are alike only when the letters and their powers match exactly.

In \(4x + 3y - 2x + y\), the \(x\) terms are \(4x\) and \(-2x\), and the \(y\) terms are \(3y\) and \(y\). Note that \(y\) means \(1y\).

Keeping the signs

The sign immediately before a term belongs to that term, and it travels with the term when you rearrange.

In \(5p - 8q - 2p\), the \(p\) terms are \(+5p\) and \(-2p\), giving \(3p\), so the answer is \(3p - 8q\).

Terms with several letters

A term such as \(ab\) is like another \(ab\) term, and \(ab\) is the same as \(ba\).

So \(3ab + 2ba\) simplifies to \(5ab\). But \(ab\) and \(a^2b\) are not alike, because the powers differ.

Key points

  • Like terms have identical letters and powers.
  • Add or subtract the coefficients only.
  • The letters do not change when collecting.
  • The sign before a term belongs to it.
  • \(y\) means \(1y\).
  • \(ab\) and \(ba\) are like terms.

Worked examples

Example 1

Simplify \(7x + 4y - 3x + 2y\).

Working

\[7x - 3x = 4x\]collect the x terms, keeping the signs
\[4y + 2y = 6y\]collect the y terms
\[4x + 6y\]write the simplified expression

Example 2

Simplify \(9a - 5b - 4a + b\).

Working

\[9a - 4a = 5a\]collect the a terms
\[-5b + b = -4b\]collect the b terms, noting b means 1b
\[5a - 4b\]write the simplified expression

Example 3

Simplify \(3x^2 + 5x - x^2 + 2x\).

Working

\[3x^2 - x^2 = 2x^2\]x squared terms are only like other x squared terms
\[5x + 2x = 7x\]collect the x terms separately
\[2x^2 + 7x\]the two groups cannot be combined further

Common mistakes

  • Combining terms with different letters.

    3x + 4y stays as it is. Only identical letters and powers can be combined.

  • Combining \(x\) and \(x^2\) terms.

    These are not like terms, so 3x² + 5x cannot be simplified to 8x³ or anything else.

  • Losing a negative sign.

    In 9a − 4a the sign belongs to the 4a. Write the signs in before collecting.

  • Forgetting that a lone letter has coefficient 1.

    In −5b + b the result is −4b, not −5b.

Exam tips

  • Underline or highlight each set of like terms in a different way.
  • Write the sign in front of every term before you start.
  • Deal with one letter at a time.
  • Check by substituting a value into both the original and simplified expressions.

Key terms

Like terms
Terms with identical letters and powers.
Simplify
To write an expression in its shortest equivalent form.
Coefficient
The number multiplying a variable.
Term
A single part of an expression separated by + or −.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.