What Is Factorisation Class 8th: A Complete NCERT Guide

Understanding Factorisation: Definition and Importance

Factorisation is a fundamental concept in Class 8 Mathematics. It means expressing a given algebraic expression as a product of its factors. These factors are simpler expressions or numbers that multiply to give the original expression.

Why is factorisation important?

• It helps simplify complex expressions.
• It is used to solve algebraic equations.
• It forms the basis for higher-level math concepts.

For example, consider the expression $x^2 - 9$. Factorisation breaks it into $(x - 3)(x + 3)$ because multiplying these two gives the original expression.

In the NCERT Class 8 syllabus, understanding factorisation is crucial for excelling in algebra and related topics.

Common Methods of Factorisation in Class 8

There are several methods to factorise expressions in Class 8. The most common ones include:

• Taking Common Factors: Extracting the greatest common factor (GCF) from all terms.
• Factorisation by Grouping: Grouping terms to find common factors.
• Using Special Formulas: Applying identities like difference of squares, perfect square trinomials, and sum/difference of cubes.

Examples:

1. Taking Common Factor:

$$ 6x^2 + 9x = 3x(2x + 3) $$

2. Difference of Squares:

$$ a^2 - b^2 = (a - b)(a + b) $$

Example: $x^2 - 16 = (x - 4)(x + 4)$

3. Perfect Square Trinomial:

$$ a^2 + 2ab + b^2 = (a + b)^2 $$

Example: $x^2 + 6x + 9 = (x + 3)^2$

Mastering these methods is essential for solving problems efficiently.

Step-by-Step Factorisation: Worked Examples

Let's solve two examples step-by-step to understand factorisation better.

Example 1: Factorise $12x^2 + 8x$

Step 1: Find the greatest common factor (GCF) of 12 and 8, which is 4.

Step 2: Find the common variable factor. Both terms have $x$, so take $x$ out.

Step 3: Write the expression as:

$$ 12x^2 + 8x = 4x(3x + 2) $$

Example 2: Factorise $x^2 - 25$

This is a difference of squares since $25 = 5^2$.

Use the formula:

$$ a^2 - b^2 = (a - b)(a + b) $$

So,

$$ x^2 - 25 = (x - 5)(x + 5) $$

These examples show how to apply factorisation methods clearly.

Comparing Factorisation Methods: When to Use Which?

Choosing the right factorisation method depends on the expression type. Here's a comparison table to help you decide:

Understanding this helps you factorise quickly and correctly.

Tips to Master Factorisation for Class 8 NCERT Exams

To excel in factorisation for your Class 8 NCERT exams, keep these tips in mind:

• Understand the basics: Don’t just memorize formulas; know why they work.
• Practice regularly: Solve all exercise questions from your NCERT textbook.
• Use diagrams and charts: Visual aids can help understand grouping and patterns.
• Check your answers: Multiply your factors to verify the original expression.
• Work on speed and accuracy: Timed practice improves exam performance.

Consistent practice and clear understanding will help you master factorisation easily.