Chapter 7 Factorisation

RD Sharma Class 8 Maths Chapter 7 – Factorisation Notes

RD Sharma class 8 Solutions for Factorisation is an important concept in algebra that helps simplify expressions and solve equations efficiently. In RD Sharma Chapter 7 of Class 8 Maths, students learn how to break down algebraic expressions into simpler factors. These notes are designed to provide a clear understanding of the methods and applications of factorisation.

Find the PDF Solutions of all the exercises in Chapter 7 – Factorisation Notes

What is Factorisation?

Factorisation is the process of expressing an algebraic expression as a product of two or more simpler expressions. These simpler expressions are called factors. For example:

x² + 5x + 6 = (x + 2)(x + 3)

Here, (x + 2) and (x + 3) are the factors of the given quadratic expression.

Key Concepts of Factorisation

1. Common Factor Method

In this method, we take out the common term from all terms in the expression.

Example:
6x + 12 = 6(x + 2)

Here, 6 is the common factor.

2. Factorisation by Grouping

When an expression has four terms, we can group them in pairs.

Example:
ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

3. Factorisation Using Identities

Algebraic identities play a crucial role in factorisation. Some important identities include:

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

Example:
x² – 9 = (x – 3)(x + 3)

4. Factorisation of Quadratic Expressions

For expressions of the form ax² + bx + c, we split the middle term.

Example:
x² + 7x + 10
= x² + 5x + 2x + 10
= x(x + 5) + 2(x + 5)
= (x + 2)(x + 5)

5. Factorisation of Expressions with Common Binomial Factor

Example:
(x + 3)(x + 5) + (x + 3)(x – 2)
= (x + 3)[(x + 5) + (x – 2)]
= (x + 3)(2x + 3)

Importance of Factorisation

Factorisation helps in simplifying algebraic expressions, solving equations, and understanding higher-level mathematics. It is widely used in polynomial division, solving quadratic equations, and even in real-life problem-solving situations.

Tips to Master Factorisation

• Always check for common factors first
• Learn algebraic identities thoroughly
• Practice splitting the middle term
• Verify your answer by multiplying the factors
• Solve a variety of problems regularly

Common Mistakes to Avoid

• Ignoring common factors
• Incorrect application of identities
• Mistakes in signs while splitting terms
• Not checking the final answer