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MathidiaMathematics Academy
Expressions and equations
Lesson 36 of 75
Introduction

Collect like terms

Objective. Simplify expressions by combining matching variable terms.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Collecting like terms means combining terms in an expression that have exactly the same variable and power, by adding or subtracting their coefficients. For example, in 5x+3y−2x+y, the x terms combine to give 3x and the y terms combine to give 4y, giving a simplified expression of 3x+4y. Terms like 2x and 2x² are not like terms because the powers differ, so they cannot be combined. Keeping track of the sign in front of each term is essential when collecting, since it travels with the term.

Worked example

Simplify the expression 7a + 3b − 4a − 5b + 2a by collecting like terms.

7 … 3
Illustrated card showing 7 … 3
  1. 1Group the a terms: 7a−4a+2a.
  2. 2Group the b terms: 3b−5b.
  3. 3Simplify each group: 7−4+2=5, so 5a; and 3−5=−2, so −2b.
  4. 4Combine into one expression.

Answer: 5a − 2b

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Common mistake. Pupils sometimes combine terms with different powers, wrongly simplifying 3x+2x² to 5x³. Check that only terms with identical variables and powers are ever combined.

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