What Is Factorisation Class 8th: Definition and Easy Methods Explained

Understanding What Is Factorisation in Class 8 Mathematics

Factorisation means writing a given algebraic expression as a product of two or more simpler expressions called factors. For example, the expression $x^2 - 9$ can be factorised as $(x - 3)(x + 3)$. This process helps simplify expressions and solve equations more easily.

In Class 8 NCERT maths, factorisation forms the foundation for algebraic manipulation. It is used to break down complex expressions into manageable parts. Knowing how to factorise correctly is essential for solving problems in algebra and geometry.

Key points:

• Factorisation converts sums or differences into products
• It helps identify common factors and patterns
• Used extensively in simplifying and solving equations

By mastering factorisation, students improve their problem-solving skills and prepare well for CBSE exams.

Common Methods of Factorisation Explained for Class 8 Students

There are several important methods to factorise algebraic expressions in Class 8. These include:

• Taking Common Factors: Extract the greatest common factor (GCF) from all terms.
• Example: $6x + 9 = 3(2x + 3)$

• Factorisation Using Special Formulas: Recognise patterns like:
• Difference of squares: $a^2 - b^2 = (a - b)(a + b)$
• Perfect square trinomials: $a^2 + 2ab + b^2 = (a + b)^2$
• Sum or difference of cubes: $a^3 \\pm b^3 = (a \\pm b)(a^2 \\mp ab + b^2)$

• Factorisation by Grouping: Group terms to find common factors.
• Example: $ax + ay + bx + by = (a + b)(x + y)$

These methods are explained with examples in the NCERT textbook. Practicing each technique helps build confidence and speed.

Step-by-Step Factorisation: Worked Examples for Class 8 NCERT

Let's solve two examples step-by-step:

Example 1: Factorise $x^2 + 5x$

• Step 1: Identify common factor: $x$
• Step 2: Write as product: $x(x + 5)$

Example 2: Factorise $x^2 - 16$

• Step 1: Recognize difference of squares: $x^2 - 4^2$
• Step 2: Apply formula: $(x - 4)(x + 4)$

These examples show how to apply methods easily. Always look for common factors first, then check for special formulas or grouping.

Why Factorisation Is Important for Class 8 Students and Exams

Factorisation is a key chapter in Class 8 NCERT mathematics because:

• It forms the basis for solving algebraic equations.
• Helps simplify expressions for easier calculations.
• Appears frequently in CBSE exam questions.
• Builds a foundation for higher classes (Class 9 and 10).

Understanding factorisation improves logical thinking and algebraic skills. Teachers recommend regular practice of NCERT exercises and solved examples to excel in exams.

Remember, factorisation is not just about memorizing formulas but understanding when and how to apply them.

Comparison of Factorisation Methods: When to Use Which?

Here is a quick comparison table to help decide which factorisation method to use:

Use this table as a quick guide during practice and exams.