🎯 Learning Objectives

By the end of this lesson, you should be able to:

   
• Identify variables, constants, and coefficients in algebraic expressions.

   
• Distinguish between "like" and "unlike" terms.

   
• Simplify algebraic expressions by collecting like terms.

   
• Expand simple algebraic expressions using the distributive law.

1. The Language of Algebra

Algebra uses letters (variables) to represent unknown numbers. An algebraic expression is a mathematical phrase that can contain numbers, variables, and operation symbols (+, -, ×, ÷).

   
• Variable: A letter representing an unknown value (e.g., x, y, a, b).

   
• Constant: A fixed number on its own (e.g., 5, -3).

   
• Coefficient: The number multiplied by the variable. In 4x, the coefficient is 4. In -y, the coefficient is -1.

2. Like and Unlike Terms

To simplify expressions, we must know the difference between like and unlike terms.

   
• Like Terms: Terms that have the exact same variables raised to the exact same powers.
  Example: 3x and 5x are like terms. 2a² and 7a² are like terms.

   
• Unlike Terms: Terms with different variables or different powers.
  Example: 3x and 3y are unlike. 4x and 4x² are unlike.

Golden Rule: You can only add or subtract like terms. You cannot add apples and oranges!

3. Simplifying Expressions

Simplifying means "collecting like terms" to make the expression as short as possible.

Example 1: Simplify 5a + 3b - 2a + 4b

   
1. Group the 'a' terms: 5a - 2a = 3a

   
2. Group the 'b' terms: 3b + 4b = 7b

   
3. Combine them: 3a + 7b

4. Expanding Brackets (Distributive Law)

When a number or variable is outside a bracket, it must be multiplied by every term inside the bracket.

Rule: a(b + c) = ab + ac

Example 2: Expand 3(x + 4)

   
• Multiply 3 by x: 3 × x = 3x

   
• Multiply 3 by 4: 3 × 4 = 12

   
• Result: 3x + 12

Example 3 (with negatives): Expand -2(y - 5)

   
• Multiply -2 by y: -2 × y = -2y

   
• Multiply -2 by -5: -2 × -5 = +10 (Remember: negative × negative = positive)

   
• Result: -2y + 10

📌 Summary

Algebra is just a set of rules for organizing information. Always check if terms are "like" before adding or subtracting them, and never forget to multiply the outside term by everything inside the bracket!