Lesson 1: Introduction to Algebraic Expressions

🎯 Learning Objectives

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

1. Define algebra and algebraic expressions.
2. Identify constants, variables, coefficients, and terms.
3. Write algebraic expressions from verbal statements.
4. Distinguish between like and unlike terms.
5. Understand basic algebraic notation and symbols.

🧾 Explanatory Notes

1. What is Algebra?
   Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. These letters are called variables because their values can change.
2. Basic Components of an Algebraic Expression
   An algebraic expression is a combination of numbers, letters, and operation signs (such as +, −, ×, ÷).

Example:
[3x + 2y - 5]
Here:

• ( x ) and ( y ) are variables.
• 3 and 2 are coefficients (numbers multiplying the variables).
• −5 is a constant term.

3. Terms in an Expression
   Each separate part of an expression joined by + or − is a term.
   Example: In ( 4a + 3b – 7 ), the terms are ( 4a, 3b, -7 ).
4. Like and Unlike Terms

• Like terms: Have the same variable(s) and power(s).
  Example: ( 3x, 5x, -2x ) are like terms.
• Unlike terms: Have different variables or powers.
  Example: ( 3x, 4y, 2x^2 ).

5. Writing Expressions from Words
   To form algebraic expressions:

• “A number increased by 5” → ( x + 5 )
• “Twice a number” → ( 2x )
• “A number decreased by 7” → ( x - 7 )
• “The sum of a number and its square” → ( x + x^2 )

✍️ Worked Examples

Example 1:
Write an algebraic expression for: “Three more than twice a number.”
Solution:
Let the number be ( x ).
“Twice a number” → ( 2x ).
“Three more than twice a number” → ( 2x + 3 ).

Example 2:
Identify the coefficients, variables, and constants in ( 4x^2 - 3x + 7 ).
Solution:

• Coefficients: 4, −3
• Variables: ( x )
• Constant: 7

Example 3:
Simplify: ( 2x + 5y + 3x - 2y ).
Solution:
Combine like terms:
( (2x + 3x) + (5y - 2y) = 5x + 3y ).