Multiplication and Division in Algebra – Combining Algebraic Terms

Basic Algebra in Full | Lesson 4

🧠 What You’ll Learn

In this lesson, you’ll learn how to multiply and divide algebraic terms — building on your understanding of addition and subtraction to handle a new family of operations.

You’ll learn how to:

  • Multiply coefficients and variables correctly in algebraic expressions
  • Understand how variables combine during multiplication, including repeated variables
  • Work confidently with powers as a result of multiplication
  • Handle multiplication involving unlike terms without confusion
  • Apply the rules of signs when multiplying and dividing positive and negative numbers
  • Simplify algebraic expressions through division by cancelling common factors
  • Convert division into multiplication to make expressions easier to simplify
  • Work through expressions that combine multiplication and division step by step
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Watch Try Exercises Solutions ✅

🧩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 $2a \times 3a$
  2. Simplify $4x \times 5x$
  3. Simplify $3y \times 2y$
  4. Simplify $6a \div 2a$
  5. Simplify $8b \div 4b$
Show Answers
  1. $6a^2$
  2. $20x^2$
  3. $6y^2$
  4. $3$
  5. $2$

  1. Simplify $2a \times 3b$
  2. Simplify $4xy \times 2y$
  3. Simplify $-5a \times 2a$
  4. Simplify $12x \div 3x$
  5. Simplify $10xy \div 5x$
Show Answers
  1. $6ab$
  2. $8xy^2$
  3. $-10a^2$
  4. $4$
  5. $2y$

  1. Simplify $3a^2 \times 2a$
  2. Simplify $5xy \times 4y^2$
  3. Simplify $-6x \times -3x$
  4. Simplify $12xy \div 4x$
  5. Simplify $\dfrac{15a^2}{5a}$
Show Answers
  1. $6a^3$
  2. $20xy^3$
  3. $18x^2$
  4. $3y$
  5. $3a$

  1. Simplify $4a \times 5b \times 3a$
  2. Simplify $-2x \times 3y \times -4x$
  3. Simplify $18xy \div 3x \times 2y$
  4. Simplify $\dfrac{20x^2y}{5xy}$
  5. Simplify $12a \times 3b \times 2a \div 6a$
Show Answers
  1. $60a^2b$
  2. $24x^2y$
  3. $12y^2$
  4. $4x$
  5. $12ab$

🔁 Continue Learning

⏮️ Back to Basic Algebra in Full
⏭️ Next Lesson →Lesson 5: Powers, Indices, Exponents, Surds & Roots in Algebra

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