Lesson 1: Algebraic Expressions – Terms, Coefficients, Simplification

🟦 Introduction

Welcome! Today, we begin an exciting journey into Algebra. Algebra is like a special language where letters and numbers work together to solve real-world problems. You may have seen things like “2x + 3” before — that’s an algebraic expression! In this lesson, you’ll learn what expressions are, how to recognize terms and coefficients, and how to simplify expressions easily. Let’s get started!

🧠 Key Concepts and Explanations

🔹 What is an Algebraic Expression?

An algebraic expression is a mathematical phrase made up of numbers, letters (called variables), and operation signs (+, -, ×, ÷) without an equals sign.

Examples: 3x + 5, 7a – 2b + 9, (2x/5) – 4

🔹 What is a Term?

A term is a single part of an algebraic expression. It could be a number, a variable, or both multiplied together.

🔹 What is a Coefficient?

The coefficient is the number placed before a variable to show how many times it is being multiplied.

Examples:

• In 5x, the coefficient is 5.
• In -2b, the coefficient is -2.

🔹 Simplifying Algebraic Expressions

Simplifying an expression means making it shorter and easier to work with by combining like terms. Like terms have the same variables raised to the same powers.

For example:

Simplify: 2x + 5x – 3

Combine like terms: 2x + 5x =

Thus, the expression becomes:

➡️ Sample Problem Walkthroughs

🔹 Example 1: Identify Terms and Coefficients

Given: 8m – 5 + 3n

• Terms: 8m, -5, 3n
• Coefficients: 8 (for 8m), 3 (for 3n)

🔹 Example 2: Simplify the Expression

Given: 4x + 7 + 2x – 5

Group like terms: 4x + 2x = and 7 – 5 = 2

Thus, final expression:

🔹 Example 3: Simplify Expressions with Brackets

Given: 3(x + 2) + 4(x – 1)

Expand the brackets:

3 × x + 3 × 2 = 3x + 6

4 × x + 4 × (-1) = 4x – 4

Now, combine like terms: 3x + 4x = and 6 – 4 = 2

Final expression:

📝 Practice Exercises

Practice 1: Simplify

Simplify the following expressions:

1. 6p + 2p – 8
2. 7y – 3y + 12
3. 9m – (3m – 5)

Practice 2: Identify Terms and Coefficients

List the terms and coefficients in:

1. 5x – 2y + 8
2. -3a + 7b – 4

Practice 3: Word Problem Challenge

A basket has x apples. John adds 3 more baskets, each with the same number of apples. Write and simplify an expression for the total number of apples.

Hint: Total apples = original + 3 × x

🔁 Recap

Today, we learned:

• Algebraic expressions combine letters, numbers, and operations.
• Terms are parts of expressions separated by + or – signs.
• Coefficients are the numbers in front of variables.
• Simplifying makes expressions shorter and easier by combining like terms.

Remember to always check for like terms when simplifying!

🪞 Reflection Prompt

Think about it: If you see “4p + 5p – 2,” what real-world situation could this represent? For example, could it be about the number of pens bought by two different people?