Basic Algebra

Grade 10 Math - Basic Algebra

Lesson Objectives

Understand the meaning of algebra and algebraic expressions.
Identify variables, constants, coefficients, and terms in an expression.
Simplify algebraic expressions using basic rules.
Apply addition, subtraction, and distribution in simplifying expressions.

Lesson Introduction

Algebra is the branch of mathematics that uses letters and symbols to represent numbers and relationships between them. It helps us generalize and solve problems more efficiently. In this lesson, we will explore how to write and simplify algebraic expressions.

Core Lesson Content

Algebraic Expression: A combination of variables, constants, and operators (like +, −, ×) without an equals sign.

Terms: Parts of an expression separated by + or −.

Coefficient: The number that multiplies a variable.

Constant: A number that stands alone without any variable.

Worked Examples

Example 1: Identify terms in

3x + 2y - 7

\text{Terms: } 3x,\ 2y,\ -7

Explanation: These are separated by plus or minus signs.

Example 2: Simplify

4x + 3x

4x + 3x = 7x

Explanation: Combine like terms with the same variable.

Example 3: Simplify

5a - 2a

5a - 2a = 3a

Explanation: Subtract coefficients of like terms.

Example 4: Simplify

3(x + 4)

3(x + 4) = 3x + 12

Explanation: Use distributive property to multiply each term inside the bracket.

Example 5: Simplify

2x + 4 - x + 3

(2x - x) + (4 + 3) = x + 7

Explanation: Group and combine like terms.

Example 6: Simplify

2(3x - 5)

2(3x - 5) = 6x - 10

Explanation: Multiply each term in the bracket by 2.

Example 7: Simplify

7x + 2y - 3x + y

(7x - 3x) + (2y + y) = 4x + 3y

Explanation: Group and combine x terms and y terms separately.

Example 8: Simplify

5(2a + 3) - 4a

5(2a + 3) = 10a + 15

10a + 15 - 4a = 6a + 15

Explanation: Distribute 5, then combine like terms.

Example 9: Simplify

x + x + x

x + x + x = 3x

Explanation: Repeated addition of same variable becomes multiplication.

Example 10: Expand and simplify

3(x + 2) - 2(x + 1)

3x + 6 - 2x - 2 = (3x - 2x) + (6 - 2) = x + 4

Explanation: Expand both brackets, then combine like terms.

Exercises

Simplify: $2x + 5x$
[NABTEC] Simplify: $6a - 2a + 4$ [Past Question]
Expand and simplify: $4(x + 3) - 2x$
[NECO] Identify terms and coefficients in $7x - 4y + 9$ [Past Question]
Find the simplified form of $8a + 3b - 2a + b$
Simplify: $5(2x + 4) - 3x$
[JAMB] Expand and simplify: $2(x - 1) + 3(x + 4)$ [Past Question]
Simplify: $4y - 2y + y$
Simplify: $a + a + a + a$
Simplify: $2(x + 3) - (x + 1)$
Simplify and group like terms: $9x - 4 + x + 6$
[WAEC] Expand: $3(2a + 5b)$ [Past Question]
Simplify: $3x + 2y - x - y$
Simplify: $4(x + 2) - 2(x - 1)$
Simplify: $7a - 3(a + 2)$

Conclusion/Recap

In this lesson, we learned the basics of algebraic expressions and how to simplify them by combining like terms and applying the distributive law. These skills are essential for solving equations and working with more advanced algebra. In our next lesson, we’ll explore how to evaluate expressions by substituting values.