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 $axy+bcxy-az-bcz$.
Given:
The given algebraic expression is $axy+bcxy-az-bcz$.
To do:
We have to factorize the expression $axy+bcxy-az-bcz$.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression means 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.
Here, we can factorize the expression $axy+bcxy-az-bcz$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $axy, bcxy, -az$ and $-bcz$.
We can group the given terms as $axy, bcxy$ and $-az, -bcz$.
Therefore, by taking $xy$ as common in $axy, bcxy$ and $-z$ as common in $-az, -bcz$, we get,
$axy+bcxy-az-bcz=xy(a+bc)-z(a+bc)$
Now, taking $(a+bc)$ common, we get,
$axy+bcxy-az-bcz=(a+bc)(xy-z)$
Hence, the given expression can be factorized as $(a+bc)(xy-z)$.
75 Views
