Simplifying and Collecting Like Terms
Like terms are terms that have exactly the same letter part, including the same power: for example, 5x and -2x are like terms, 3y and 7y are like terms, but 5x and 5x^2 are not like terms. Simplifying an expression by collecting like terms means adding or subtracting the coefficients of each group of like terms, while unlike terms are left separate and unchanged.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the letter part of each term, including any power, to decide which terms are like each other.
- Group like terms together mentally or by underlining them, keeping the sign written directly in front of each term.
- Add or subtract the coefficients within each group of like terms.
- Leave unlike terms (different letters, or the same letter to a different power) unsimplified and written separately.
- Write the simplified expression, usually ordering terms from the highest power down to the constant.
- Check the answer by substituting a chosen number for each letter into both the original and simplified expressions - the two results should match.
Worked example
Simplify fully: 5x + 3y - 2x + 7y - 4.
- Identify the like terms: 5x and -2x are like terms; 3y and 7y are like terms; -4 is a constant with no like partner.
- Collect the x terms: 5x - 2x = 3x.
- Collect the y terms: 3y + 7y = 10y.
- Write the constant term as it is: -4.
- Combine all the collected terms: 3x + 10y - 4.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Simplify 6a + 5a.Show answer
Answer: 11a
Q2Simplify 9b - 4b + 2b.Show answer
Answer: 7b
Q3Simplify 4x + 3y + 2x - y.Show answer
Answer: 6x + 2y
Q4Simplify 5p^2 + 3p - 2p^2 + p.Show answer
Answer: 3p^2 + 4p
Q5Simplify 7 + 2x - 5 + 6x.Show answer
Answer: 8x + 2
Q6Simplify 3ab + 2a - ab + 5a.Show answer
Answer: 2ab + 7a
Q7Simplify 10y - 3x - 4y + x.Show answer
Answer: 6y - 2x
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Simplify fully: 8m + 3n - 5m - n + 6.
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Simplify fully: 4x^2 + 3x - x^2 + 5x - 2.
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Free printable worksheet
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This topic is chapter 20 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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