Class 8 Mathematics – Algebraic Expressions and Identities

1. Introduction

• Algebraic expressions are combinations of numbers, variables, and arithmetic operations.

• Variables represent unknown values.

• Identities are algebraic statements that are true for all values of the variables.

Key Concept:

• Algebra helps in solving problems, generalizing patterns, and forming formulas.

2. Types of Algebraic Expressions

3. Key Operations on Algebraic Expressions

1. Addition and Subtraction – Combine like terms only.

2. Multiplication – Multiply each term of one expression with every term of the other.

3. Factorization – Writing an expression as a product of simpler expressions.

4. Substitution – Replacing variables with numbers to evaluate the expression.

Key Concept:

• Like terms have same variables with same powers.

• Factorization helps in simplifying expressions and solving equations.

4. Algebraic Identities (Conceptual)

• Identities are equalities that hold true for all values of the variables.

• They are used to simplify expressions and calculations.

Common Types (Conceptual):

1. Square of a sum: Sum multiplied by itself.

2. Square of a difference: Difference multiplied by itself.

3. Difference of squares: Difference between two perfect squares.

4. Cube of a sum or difference: Multiplying cube expressions.

Key Concept:

• Identities help in quick calculation, factorization, and problem-solving.

5. Applications

• Simplifying complex expressions.

• Solving algebraic equations.

• Factoring expressions for quadratic problems.

• Useful in geometry, physics, and real-life calculations.

6. Key Points to Remember

• Algebraic expressions: Numbers + variables + operations.

• Like terms must have same variables and powers.

• Identities are always true, regardless of variable values.

• Operations include addition, subtraction, multiplication, factorization, and evaluation.

• Algebraic concepts are foundational for higher mathematics.