What is Factorisation Class 8: Complete Guide for NCERT Students

Understanding Factorisation in Class 8 Mathematics

Factorisation is a key topic in Class 8 NCERT Mathematics. It involves rewriting algebraic expressions as a product of simpler expressions called factors. For example, the expression $x^2 + 5x$ can be factorised as $x(x + 5)$. This process helps in simplifying expressions and solving equations effectively.

In simple terms, factorisation means "breaking down" an expression into parts that multiply to give the original expression. It is the reverse process of expansion.

Why is factorisation important?

• Simplifies algebraic expressions
• Helps solve equations quickly
• Essential for higher mathematics

Class 8 students should focus on understanding the basic methods and identities used in factorisation to build a strong foundation.

Common Methods of Factorisation Explained

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

• Taking Common Factors: Extract the greatest common factor (GCF) from all terms.
• Factorising Trinomials: Expressions like $ax^2 + bx + c$ can be factorised into two binomials.
• Difference of Squares: Use the identity $a^2 - b^2 = (a - b)(a + b)$.
• Perfect Square Trinomials: Recognise and factor expressions like $a^2 + 2ab + b^2 = (a + b)^2$.

Example: Taking Common Factors

Factorise $12x^3 + 8x^2$.

• Find GCF: $4x^2$
• Factorised form: $4x^2(3x + 2)$

Example: Difference of Squares

Factorise $x^2 - 16$.

• Recognise $16 = 4^2$
• Apply identity: $(x - 4)(x + 4)$

Understanding these methods helps solve a wide range of algebra problems.

Special Factorisation Formulas to Remember

Class 8 NCERT Maths introduces important algebraic identities used in factorisation. Memorising these formulas makes factorisation easier and faster.

Worked Example

Factorise $x^2 - 25$.

• Recognise $25 = 5^2$
• Apply difference of squares: $x^2 - 5^2 = (x - 5)(x + 5)$

These formulas are vital for solving factorisation problems quickly in exams.

Step-by-Step Factorisation of Algebraic Expressions

To factorise any algebraic expression, follow these steps:

1. Look for a Common Factor: Check if all terms share a common factor. 2. Apply Special Formulas: Use identities like difference of squares or perfect square trinomials. 3. Break Down Complex Expressions: Split middle terms or rearrange terms if needed. 4. Verify by Expansion: Multiply factors to confirm the original expression.

Example

Factorise $2x^2 + 8x$.

• Step 1: Common factor is $2x$
• Step 2: Factor out $2x$: $2x(x + 4)$

Another Example

Factorise $x^2 + 7x + 12$.

• Step 1: Find two numbers that multiply to 12 and add to 7: 3 and 4
• Step 2: Write as $(x + 3)(x + 4)$

Following these steps helps in systematic factorisation and reduces errors.

Comparing Factorisation Methods: Which to Use When?

Choosing the right factorisation method depends on the expression type. Here's a quick comparison:

Understanding these helps select the fastest method for factorisation problems.

Practical Tips to Master Factorisation for Class 8 Exams

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

• Practice Regularly: Solve varied problems to build confidence.
• Memorise Key Formulas: Special identities speed up factorisation.
• Check Your Work: Always expand factors to verify correctness.
• Understand, Don’t Memorise: Know why each method works.
• Use Stepwise Approach: Break down complex expressions carefully.

Consistent practice and understanding will make factorisation easier and improve your exam scores.