Class 8 Mathematics – Factorization

1. Introduction

• Factorization is the process of breaking down an algebraic expression into simpler expressions (called factors) that, when multiplied together, give the original expression.

• It is the reverse process of multiplication.

Key Concept:

• Factorization helps in simplifying expressions, solving equations, and checking divisibility.

2. Factors and Multiples (Conceptual)

• Factors: Numbers or expressions that divide a given number or expression exactly.

• Multiples: Numbers or expressions obtained by multiplying the given number or expression.

• Factorization focuses on finding factors.

Example Concept:

• Think of a rectangle: area = length × breadth → length and breadth are the factors of the area.

3. Methods of Factorization (Conceptual)

1. Taking out the Common Factor

   • Identify terms that share a common number or variable.

   • Factor it out to simplify the expression.

2. Factorization by Grouping

   • Group terms in pairs or sets.

   • Take common factors from each group and then combine.

3. Using Algebraic Identities

   • Identities like square of sum, square of difference, difference of squares help to factor quickly.

4. Special Factorization Cases

   • Cubic expressions can be factored using special patterns like sum or difference of cubes.

4. Applications of Factorization

• Solving Equations: Factorization converts complex equations into simpler ones.

• Simplifying Algebraic Expressions: Makes calculations easier.

• Real-Life Problems: Distribution, area problems, and arranging objects efficiently.

• Mathematics Competitions: Factorization is a fundamental skill for problem-solving.

5. Key Points to Remember

• Factorization = writing an expression as a product of simpler expressions.

• Look for a common factor first.

• Use grouping and identities for complex expressions.

• Helps in solving, simplifying, and analyzing expressions.

• Factorization is the foundation for algebra and higher mathematics.