- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Factorize the expression $3x^3y-243xy^3$.
Given:
The given algebraic expression is $3x^3y-243xy^3$.
To do:
We have to factorize the expression $3x^3y-243xy^3$.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution.
An algebraic expression is factored completely when it is written as a product of prime factors.
$3x^3y-243xy^3$ can be written as,
$3x^3y-243xy^3=3xy(x^2-81y^2)$ (Taking $3xy$ common)
$3x^3y-243xy^3=3xy[(x)^2-(9y)^2]$ [Since $81=(9)^2$]
Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression.
Therefore,
$3x^3y-243xy^3=3xy[(x)^2-(9y)^2]$
$3x^3y-243xy^3=3xy(x+9y)(x-9y)$
Hence, the given expression can be factorized as $3xy(x+9y)(x-9y)$.
53 Views
