NCERT Solutions for Class 8 Maths Chapter 14 Factorization

Algebra often feels like a puzzle where the pieces are numbers and variables. For many students, going from fundamental maths to algebraic expressions is a big problem. factorization, or figuring out how to "undo" multiplication, is one of the hardest things to do. You are not the only one who has ever been trapped when staring at a long equation like ax^2 + bx. This is why the class 8 maths chapter 14 pdf solutions are so useful.

The main purpose of class 8 maths chapter factorization is to teach you how to break down a complicated expression into its simplest 'factors'. Algebraic expressions can be split down into smaller, easier-to-handle parts, just like how 12 can be expressed as 3 times 4. Getting good at these factorization class 8 solutions is not just important for passing your school tests; it's also a basic skill you'll need for more advanced maths, physics, and engineering. We give you detailed, step-by-step instructions in this guide to help you do well on every exercise.

With our class 8 maths chapter 14 solutions, you may learn how to use algebraic expressions. Find out how to break down expressions using identities, common factors, and regrouping.

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NCERT Solutions for Class 8 Maths chapter - 14 Factorisation

NCERT Solutions for Class 8 Maths Exercise 14.1

Question 1.
Find the common factors of the given terms.


Solution :
(i) 12x = 2 × 2 × 3

36 = 2 × 2 × 3 × 3

Hence, the common factors are 2, 2 and 3 = 2 × 2 × 3 = 12
(ii)   2y = 2 ×y

22xy = 2 × 11 × x × y

Hence the common factors are
2 and y  =  2 × y = 2y

(iii) 14 pq = 2×7× p × q

Question 2.
Factorize the following expressions.


Solution :




Taking common factors from each term,

Question 3.
Factorize:


Solution :


Read More: NCERT Solution for Class 8 Maths Chapter 1 Rational Numbers

NCERT Solutions for Class 8 Maths Exercise 14.2
Question 1.
Factorize the following expressions:



Solution :




Question 2.
Factorize
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Solution :


Question 3.
Factorize the expressions:


Solution :




Question 4.
Factorize:

Solution :

(iv)



Question 5.
Factorize the following expressions:


Solution :

Read More: NCERT Solution for Class 8 Maths Chapter 2

NCERT Solutions for Class 8 Maths Exercise 14.3
Question 1.
Carry out the following divisions:


Solution :




Question 2.
Divide the given polynomial by the given monomial:


Solution :




Question 3.
Work out the following divisions:



Solution :



(iii)


Solution :








Solution :



Question 13.



Solution :


Solution :
L.H.S. =R.H.S.

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What do you mean by "Factorization"?

In class 8 maths chapter 14 solutions, factorization is defined as the process of expressing an algebraic statement as a product of its components.  These factors can be numbers, letters, or even equations in algebra. 

Methods of factorization

There are four main methods in NCERT Class 8 factorization solutions:

1. Common Factor Method: Finding a phrase that is in every part of the expression.

2. Regrouping Terms: Putting terms into pairs to find what they have in common.

3. Using Identities: Using easy-to-remember equations like (a + b)^2 or (a^2 - b^2).

4. Splitting the Middle Term: This is usually used for quadratic expressions.

Exercises in Class 8 Maths Chapter 14 Factorization Solutions

We've broken down the main ideas in the class 8 mathematics chapter 14 pdf solutions to help you study better. 

1. The Method of Common Factors

This is the easiest way to factor. You look for the Highest Common Factor (HCF) of all the terms.

For example, factor 5x + 10.

The answer is that 5 is the common factor. So, 5(x + 2).

2. Using Algebraic Identities

You need to be able to see patterns in order to answer many of the problems in the factorization class 8 ncert solutions.

• Identity 1: (a + b)^2 = a^2 + 2ab + b^2

• Identity 2: (a - b)^2 = a^2 - 2ab + b^2

• Identity 3: (a + b)(a - b) = a^2 - b^2

3. Dividing Algebraic Expressions

• One of the most important things to do in class 8 maths chapter 14 is how to divide a polynomial by a monomial or another polynomial.

Rule: Break down both the top and bottom numbers into their prime factors, and then get rid of the ones that are the same.

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Summary Table of Factorisation Class 8 Solutions

 Class 8 Maths Chapter 14 factorization formulas  for quick review:

Benefits of Using Class 8 Mathematics Chapter 14 Factorization Solutions?

There are many benefits to using structured factorization class 8 solutions:

• Logical Progression: The chapter begins with simple monomials and goes on to more complicated polynomials. 

• Accuracy in the test: Following the NCERT pattern makes sure you give the steps that the test makers expect.

• Conceptual Clarity: You don't just memorise; you know the "why" behind regrouping and separate phrases. 

Tips for Doing Class 8 Maths Chapter 14 Solutions

• Look for Common Factors First: Always check if there is a number or variable you can pull out before trying complex identities.

• Check Your Signs: A common mistake in the factorization chapter of eighth-grade arithmetic is getting the plus and minus signs mixed up, especially with Identity 2.

• Multiply to Verify: If you're not confident about your solution, multiply the factors again. You should acquire the original phrase!

Class 8 Maths Chapter 14 Solutions FAQs

1. What is the difference between a factor and factorization?

A factor is a number or expression that divides another number or expression perfectly. factorization is the process of finding all the factors of a statement. We use several examples in our class 8 mathematics chapter 14 solutions to show this difference.

2. When should I use the regrouping method?

If you can't find a common factor for all the terms, but you can find one when you group the terms together, you should employ regrouping. This is a very important part of the class 8 NCERT solutions for factorization.

3. How can I break down x^2 - 9?

The "Difference of Squares" identity, which is a^2 - b^2, is the same as this. Because 3^2 is the same as 9, the formula changes to (x + 3)(x - 3).  The class 8 mathematics chapter 14 pdf solutions have additional instances like this.

4. Is factorization used in daily life?

Yes! factorization is used in cryptography (to keep your internet data safe), engineering (to figure out how much stress a structure can handle), and financial modelling (to make complicated interest calculations easier).

5. Where can I find the complete class 8 maths chapter 14 solutions?

You can find comprehensive, step-by-step ncert class 8 factorization solutions on the Physics Wallah website (PW Store), which are designed to help students master school exams and competitive foundations.