Lesson 2: Expansion and Factorization of Expressions

👨🏽‍🏫 Introduction

Imagine you’re packing gift bags for a party 🎁. If each bag has 3 sweets and 2 biscuits, and you have x bags, the total can be written as . When you open the brackets, you get — this is called expansion.

On the other hand, if you have and you want to simplify or “compress” it by finding what’s common, you get — this is factorization.

Let’s explore both processes and understand how to move smoothly between expanded and factored forms of algebraic expressions.

By the end of this lesson, you will:

• Expand brackets using distributive law
• Factor expressions by taking out the common factor
• Recognize and use special identities like and

🧠 Key Concepts

✖️ 1. Expansion of Expressions

To expand means to multiply out brackets and simplify the expression.

🧾 Distributive Law:

Examples:

🧮 Special Identities

📦 2. Factorization of Expressions

To factorize means to write an expression as a product of its factors — basically, putting it back into brackets.

Step 1: Find the Highest Common Factor (HCF)
Look for what each term shares and take it outside the bracket.

Examples:

Step 2: Use Identities (if possible)

🧮 Sample Problem Walkthroughs

1. Expand:
   Multiply 5 by each term inside the bracket:
   
2. Expand:
   Use identity:
   So:
3. Factorize:
   HCF is 4:
4. Factorize:
   This is a difference of squares:
   
5. Factorize:
   This is a perfect square:

✍🏽 Practice Exercises

🅰️ A. Expand the following expressions:

🅱️ B. Factorize the following expressions:

✅ Answers and Explanations

• A1:
• A2:
• A3:

• B1:
• B2:
• B3:

📌 Recap

• ✅ To expand means to remove brackets by multiplying
• ✅ Use the distributive law and special identities to simplify expressions
• ✅ To factorize means to take out common factors or use identities to rewrite expressions in bracketed form
• ✅ Recognize perfect square trinomials and difference of squares

💭 Reflection Prompt

Think about your school or home chores. If you sweep 2 rooms a day for 5 days, the total is like . Can you write it as an expression, then expand and simplify it? What other situations in your life involve repeated groups or steps?