Class 8 Maths – Chapter 9

Algebraic Expressions & Identities

STEP 1: Concept Notes

🔹 What is an Algebraic Expression?

An algebraic expression is a combination of variables, numbers and operations (+, −, ×).

Examples:

• 2x
• 3x + 5
• 4a − 7
• 5x² + 2x − 1

🔹 Terms of an Expression

Each part of an expression separated by + or − is called a term.

Example: 3x + 5 − 2y

• 3x → term
• 5 → term
• −2y → term

🔹 Coefficient

The numerical part of a term is called the coefficient.

Example: In 7x, coefficient of x = 7

Example: In −5a, coefficient of a = −5

🔹 Like and Unlike Terms

Like Terms: Terms having the same variable and same power.

Example: 3x, −7x, 10x

Unlike Terms: Terms having different variables or powers.

Example: 2x, 3y, 5x²

🔹 Types of Algebraic Expressions

• Monomial: One term (Example: 5x)
• Binomial: Two terms (Example: x + 3)
• Trinomial: Three terms (Example: x² + 2x + 1)

🔹 Algebraic Identities

Algebraic identities are formulas which are true for all values of variables.

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• (a + b)(a − b) = a² − b²

✏️ Simple Example

Expand: (x + 2)²

Solution:
(x + 2)² = x² + 2×x×2 + 2²
= x² + 4x + 4