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
FAQs for RD Sharma Class 8 Maths Chapter 7 Factorisation
The easiest method to begin with is the common factor method. It involves identifying the greatest common factor among all the terms in an expression and factoring it out. This method builds a strong foundation for understanding more complex techniques like grouping and using identities. Once students are comfortable with identifying common factors, they can gradually move to factorising quadratic expressions and applying algebraic identities. Consistent practice and solving simple examples help in building confidence and accuracy in factorisation.
Factorisation is important because it simplifies complex algebraic expressions and makes them easier to solve. It is widely used in solving equations, especially quadratic equations, and plays a key role in higher mathematics topics. By breaking expressions into factors, students can better understand the structure of equations and find solutions more efficiently. Factorisation is also useful in real-life applications such as problem-solving in physics, engineering, and economics. Mastering this concept ensures a strong algebraic foundation for future studies.
Improving factorisation skills requires consistent practice and a clear understanding of basic concepts. Start by learning algebraic identities and practising problems based on them. Focus on different types of factorisation methods, such as common factor, grouping, and splitting the middle term. Try solving a variety of problems with increasing difficulty levels. Reviewing mistakes and understanding where errors occur is also essential. Regular revision and practicing sample questions help reinforce concepts and improve speed and accuracy over time.