- 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 each of the following expressions:$(a - 2b)^3 - 512b^3$
Given:
$(a - 2b)^3 - 512b^3$
To do:
We have to factorize the given expression.
Solution:
We know that,
$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$
$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
Therefore,
$(a - 2b)^3 - 512b^3 = (a - 2b)^3 - (8b)^3$
$= (a - 2b - 8b) [(a - 2b)^2 + (a - 2b) \times 8b + (8b)^2]$
$= (a - 10b) [a^2 + 4b^2 - 4ab + 8ab - 16b^2 + 64b^2]$
$= (a - 10b) (a^2 + 4ab + 52b^2)$
Hence, $(a - 2b)^3 - 512b^3 = (a - 10b) (a^2 + 4ab + 52b^2)$.
Advertisements
To Continue Learning Please Login
Login with Google