Collecting Like Terms in Algebra

Basic Algebra in Full | Lesson 2

🧠 What You’ll Learn

In this lesson, you’ll learn how to collect like terms to make algebra simpler and clearer.

You’ll learn how to:

  • Spot like terms and group them together
  • Know when you can and cannot collect terms
  • Understand that signs (like + and −) belong to each term
  • See how different types of operations affect what you can do
  • Move terms correctly by changing their signs
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🧩Practice Exercises

These exercises help you build from foundation to advanced understanding.

You can:

  • Start at your level
  • Or work through all levels step by step

✍️ Attempt exercises before checking answers.

🎯 Levels

Each level matches a stage of learning and shows
what you should be able to understand and solve at that point.

🟢 Foundation → You’re learning this topic for the first time
🟠 Developing → You understand the basics and are building on them
⚪ Confident → You’re ready for deeper, multi-step problems
⚫ Advanced → You want to challenge your understanding further

📘 Not sure where you fit? → View Level Guide

💡 Each set of exercises is designed to match what students at that stage are typically expected to handle.

Start with your level, then try the next one when you feel ready.

Collect the like terms in each expression.

  1. $3x + 5x + 2$
  2. $7y – 4y + 6$
  3. $2a + 3b + 5a + b$
  4. $9m – 2 + 4m + 7$
  5. $6x + 3y – 2x + y – 5$
Show Answers
  1. $3x + 5x + 2$
  2. $7y – 4y + 6$
  3. $2a + 5a + 3b + b$
  4. $9m + 4m – 2 + 7$
  5. $6x – 2x + 3y + y – 5$

Collect the like terms in each expression.

  1. $5x^2 + 3x + 2x^2 – x$
  2. $4a + 6 – 2a + 9$
  3. $7y^2 + 3y – 5y^2 + y – 8$
  4. $3ab + 2a – ab + 5a$
  5. $8x^2 + 4x – 3 + 2x^2 – x + 7$
Show Answers
  1. $5x^2 + 2x^2 + 3x – x$
  2. $4a – 2a + 6 + 9$
  3. $7y^2 – 5y^2 + 3y + y – 8$
  4. $3ab – ab + 2a + 5a$
  5. $8x^2 + 2x^2 + 4x – x – 3 + 7$

Collect the like terms in each expression.

  1. $6x^2y + 3xy – 2x^2y + 5xy – 4$
  2. $9a^2 – 3a + 7 – 4a^2 + a – 2$
  3. $5xy^2 + 2x^2y – 3xy^2 + x^2y + 6$
  4. $8m^3 – 2m^2 + 5m^3 + m^2 – 7$
  5. $4x^2 + 3xy + 2 – x^2 + 5xy – 6$
Show Answers
  1. $6x^2y – 2x^2y + 3xy + 5xy – 4$
  2. $9a^2 – 4a^2 – 3a + a + 7 – 2$
  3. $5xy^2 – 3xy^2 + 2x^2y + x^2y + 6$
  4. $8m^3 + 5m^3 – 2m^2 + m^2 – 7$
  5. $4x^2 – x^2 + 3xy + 5xy + 2 – 6$

Collect like terms after moving specified terms as instructed.

  1. Move all $x^2y$ and $xy$ terms to the left:
    $5x^2y – 3xy = 2x^2y + 4xy + 6$
  2. Move all $a^2$ and $a$ terms to the left:
    $7a^2 + 3a + 5 = 2a^2 – a + 9$
  3. Move all $xy^2$ and $x^2y$ terms to the left:
    $4xy^2 + 2x^2y = xy^2 – 3x^2y + 8$
  4. Move all $m^2$ and $m$ terms to the left:
    $6m^2 – 4m + 7 = 2m^2 + 3m – 5$
  5. Move all $x^2y$ and $xy$ terms to the left:
    $9x^2y – 5xy + 4 = 3x^2y + 2xy – 6$
Show Answers
  1.  $5x^2y – 3xy – 2x^2y – 4xy = 6$
  2. $7a^2 – 2a^2 + 3a + a + 5 = 9$
  3. $4xy^2 – xy^2 + 2x^2y + 3x^2y = 8$
  4. $6m^2 – 2m^2 – 4m – 3m + 7 = -5$
  5. $9x^2y – 3x^2y – 5xy – 2xy + 4 = -6$

🔁 Continue Learning

⏮️ Back to Basic Algebra in Full
⏭️ Next Lesson → Lesson 3: Addition & Subtraction in Algebra

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