Class 9 Exam > Class 9 Notes > RD Sharma Solutions for Class 9 Mathematics > RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths
Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download
Q 1 . 64a3+125b3+240a2b+300ab2
SOLUTION :
= (4a)3+(5b)3+3(4a)2(5b)+3(4a)(5b)2 [∵a3+b3+3a2b+3ab2=(a+b)3]
= (4a+5b)3
= (4a+5b)(4a+5b)(4a+5b)
∴ 64a3+125b3+240a2b+300ab2 = (4a+5b)(4a+5b)(4a+5b)
Q 2 . 125x3−27y3−225x2y+135xy2
SOLUTION :
= (5x)3−(3y)3−3(5x)2(3y)+3(5x)(3y)2 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(5x−3y)3
=(5x−3y)(5x−3y)(5x−3y)
∴ 125x3−27y3−225x2y+135xy2 = (5x−3y)(5x−3y)(5x−3y)
Q 3 .
SOLUTION :
[∵x3+b3+3x2b+3xb2=(x+b)3]
Q 4 . 8x3+27y3+36x2y+54xy2
SOLUTION :
= (2x)3+(3y)3+3×(2x)2×3y+3×(2x)(3y)2
= (2x+3y)3 [ ∵ a³ + b³ + 3a²b + 3ab² = (a + b) ³]
=(2x+3y)(2x+3y)(2x+3y)
∴ 8x3+27y3+36x2y+54xy2 = (2x+3y)(2x+3y)(2x+3y)
Q 5 . a3−3a2b+3ab2−b3+8
SOLUTION :
= (a−b)3+23 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(a−b+2)((a−b)2−(a−b)2+22) ∵[a3+b3=(a+b)(a2−ab+b2)]
=(a−b+2)(a2+b2−2ab−2(a−b)+4)
=(a−b+2)(a2+b2−2ab−2a+2b+4)
∴ a3−3a2b+3ab2−b3+8 = (a−b+2)(a2+b2−2ab−2a+2b+4)
Q 6 . x3+8y3+6x2y+12xy2
SOLUTION :
= (x)3+(2y)3+3×x2×2y+3×x×(2y)2
= (x+2y)3 [∵x3+y3+3x2y+3xy2=(x+y)3]
=(x+2y)(x+2y)(x+2y)
∴ x3+8y3+6x2y+12xy2 = (x+2y)(x+2y)(x+2y)
Q 7 . 8x3+y3+12x2y+6xy2
SOLUTION :
= (2x)3+(y)3+3×(2x)2×y+3(2x)×y2
= (2x+y)3 [∵a3+b3+3a2b+3ab2=(a+b)3]
=(2x+y)(2x+y)(2x+y)
∴ 8x3+y3+12x2y+6xy2 = (2x+y)(2x+y)(2x+y)
Q 8 . 8a3+27b3+36a2b+54ab2
SOLUTION :
= (2a)3+(3b)3+3×(2a)2×3b+3×2a×(3b)2
= (2a+3b)3 [∵a3+b3+3a2b+3ab2=(a+b)3]
=(2a+3b)(2a+3b)(2a+3b)
∴ 8a3+27b3+36a2b+54ab2 =(2a+3b)(2a+3b)(2a+3b)
Q 9 . 8a3−27b3−36a2b+54ab2
SOLUTION :
= (2a)3−(3b)3−3×(2a)2×3b+3×2a×(3b)2
= (2a–3b)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(2a–3b)(2a–3b)(2a–3b)
∴ 8a3−27b3−36a2b+54ab2 =(2a–3b)(2a–3b)(2a–3b)
Q 10 . x3−12x(x−4)−64
SOLUTION :
= x3−12x2+48x−64
= x3−3×x2×4+3×42×x−43
= (x−4)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(x−4)(x−4)(x−4)
∴ x3−12x(x−4)−64 =(x−4)(x−4)(x−4)
Q 11 . a3x3−3a2bx2+3ab2x−b3
SOLUTION :
= (ax)3−3(ax)2×b+3(ax)×b2−b3
= (ax−b)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(ax−b)(ax−b)(ax−b)
∴ a3x3−3a2bx2+3ab2x−b3 =(ax−b)(ax−b)(ax−b)
The document Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
All you need of Class 9 at this link: Class 9
FAQs on Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics
| 1. What is factorization of algebraic expressions? |  |
Ans. Factorization of algebraic expressions involves breaking down an algebraic expression into its constituent factors. It helps in simplifying complex expressions and solving equations more easily.
| 2. How do you factorize an algebraic expression? | |
Ans. To factorize an algebraic expression, we look for common factors among the terms and then use various methods like taking out the common factor, using identities, or using specific factorization formulas to break down the expression into factors.
| 3. Why is factorization important in mathematics? | |
Ans. Factorization is important in mathematics as it helps in simplifying complex expressions, solving equations, finding common factors, and identifying patterns. It also plays a crucial role in many mathematical concepts like simplifying fractions, finding roots of quadratic equations, and solving problems related to algebraic identities.
| 4. Can you explain the difference between factorization and expansion of algebraic expressions? | |
Ans. Factorization and expansion are opposite operations. Factorization involves breaking down an expression into its factors, while expansion involves multiplying factors to get the original expression. Factorization simplifies an expression, whereas expansion expands it to its original form.
| 5. What are some common factorization formulas used in algebra? | |
Ans. Some common factorization formulas used in algebra include the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), the perfect square trinomial formula (a^2 + 2ab + b^2 = (a + b)^2), and the difference of cubes formula (a^3 - b^3 = (a - b)(a^2 + ab + b^2)). These formulas help in factorizing specific types of algebraic expressions.
Related Exams
About this Document
|
4.92/5 Rating |
|
Nov 24, 2024 Last updated |
Document Description: RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths for Class 9 2024 is part of RD Sharma Solutions for Class 9 Mathematics preparation.
The notes and questions for RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths have been prepared according to the Class 9 exam syllabus. Information about RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths covers topics
like and RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Example, for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths.
Introduction of RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths in English is available as part of our RD Sharma Solutions for Class 9 Mathematics
for Class 9 & RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths in Hindi for RD Sharma Solutions for Class 9 Mathematics course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics
Description
Full syllabus notes, lecture & questions for Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics - Class 9 | Plus excerises question with solution to help you revise complete syllabus for RD Sharma Solutions for Class 9 Mathematics | Best notes, free PDF download
Information about RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths
In this doc you can find the meaning of RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths defined & explained in the simplest way possible. Besides explaining types of
RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths tests, examples and also practice Class 9
tests
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
MCQs
,Semester Notes
,Exam
,Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics
,Free
,Factorization Of Algebraic Expressions
,shortcuts and tricks
,video lectures
,Extra Questions
,Viva Questions
,Class 9
,Class 9
,Objective type Questions
,Class 9
,Summary
,mock tests for examination
,Previous Year Questions with Solutions
,Factorization Of Algebraic Expressions
,Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics
,study material
,past year papers
,ppt
,Ex-5.3
,Ex-5.3
,Factorization Of Algebraic Expressions
,Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics
,Ex-5.3
,Sample Paper
,practice quizzes
,Important questions
;
Additional Information about RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths for Class 9 Preparation
RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Free PDF Download
The RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths now and kickstart your journey towards success in the Class 9 exam.
Importance of RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths
The importance of RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Notes
RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Notes on EduRev are your ultimate resource for success.
RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Class 9 Questions
The "RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths on the App
Students of Class 9 can study RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup