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
Factorise each of the following:
$( i)$. $8a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$
$( iii)$. $27-125 a^{3}-135a+225a^{2}$
Given: $( i)$. $8a^{3}+b^{3}+12 a^{2} b+6 a b^{2}$ $( ii)$. $27-125 a^{3}-135 a+225 a^{2}$
To do: To factorise the given polynomial.
Solution:
$( i).$ $8a^3 + b^3 + 12a^2b + 6ab^2$
$= ( 2a)^3 + ( b)^3 + 3( 2a)( b)( 2a + b)$
$= ( 2a + b)^3$ [$\because a^3 + b^3 + 3ab( a + b) = ( a + b)^3$]
$( ii)$. $27-125a^3-135a+225a^2$
$=125a3-225a2+135a-27$
$=(5a)3+(-3)3+3(5a)(-3)(5a-3)$
$=( 5a-3)^3$ [$\because a^3-b^3-3ab( a-b)=( a-b)^3$]
Updated on: 10-Oct-2022
32 Views
Advertisements