Removing Brackets in Algebra – The Distributive Law Explained

Basic Algebra in Full | Lesson 6

🧠 What You’ll Learn

In this lesson, you’ll understand how brackets work in algebra and how they help you organize, interpret, and simplify expressions correctly; from basic grouping to more advanced expansion techniques.

You’ll learn how to:

• Understand what brackets represent as grouped units in expressions
• Interpret brackets correctly using the order of operations
• Insert brackets into expressions meaningfully without changing their value
• Avoid common mistakes when placing brackets, especially with negative terms
• Understand the idea of operator ownership and how signs affect grouped terms
• Apply the Distributive Law to expand and remove brackets correctly
• Handle expressions with a plus or minus before a bracket
• Work with multiplication and division involving brackets
• Simplify expressions involving nested brackets step by step
• Translate word problems into algebraic expressions using brackets correctly

By the end, you’ll be able to confidently create, interpret, and remove brackets while maintaining mathematical accuracy and clarity.

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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.

  1. Simplify $4 + (2 \times 5) – 3$
  2. Insert brackets to show grouping, then simplify: $3x + 2x + 4y + 5y$
  3. Expand and simplify: $2(x + 6)$
  4. Expand and simplify: $5(3x – 2)$
  5. Simplify: $7 + (x + 4)$
Show Answers
  1.  $11$
  2. $5x + 9y$
  3. $2x + 12$
  4. $15x – 10$
  5. $x + 11$

  1. Expand and simplify: $3(2x + 5) + (x + 4)$
  2. Expand and simplify: $6y – (2y + 7)$
  3. Insert brackets correctly, then simplify: $4x + 3x – 5y + 2y$
  4. Expand and simplify: $-4(a – 3)$
  5. Translate into an expression using brackets, then simplify: “Add $5$ to a number $x$, then multiply by $2$”
Show Answers
  1. $7x + 19$
  2. $4y – 7$
  3. $7x – 3y$
  4. $-4a + 12$
  5. $2(x + 5) = 2x + 10$

  1. Expand and simplify: $5(x + 2) – (3x – 4)$
  2. Simplify: $8 + 2(x + 3)$
  3. Expand and simplify: $7a – (2a – 5b + 6)$
  4. Simplify fully: $3(x + 4) + 2(x – 1)$
  5. Simplify (brackets inside brackets): $2\big(x – (3y + 2)\big)$
Show Answers
  1. $2x + 14$
  2. $2x + 14$
  3. $5a + 5b – 6$
  4. $5x + 10$
  5. $2x – 6y – 4$

  1. Simplify: $4x + 3(x – (2x – 5))$
  2. Expand and simplify: $-2\big(3a – (2a – 4b + 1)\big)$
  3. Simplify: $5(x + 2y) – 3(x – y) + (2x + y)$
  4. Simplify fully: $3\big(2x – (x – (3y – 2))\big)$
  5. Translate and simplify: “Multiply the result of subtracting $3$ from $x$ by $4$, then subtract the result of adding $2$ to $x$”
Show Answers
  1.  $5x + 15$
  2. $-2a – 8b + 2$
  3. $4x + 14y$
  4. $3x + 9y – 6$
  5. $4(x – 3) – (x + 2) = 3x – 14$

🔁 Continue Learning

⏮️ Back to Basic Algebra in Full
⏭️ Next Lesson → Lesson 7: Algebraic Fractions

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