- 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
Simplify each of the following products:
\( (2 x^{4}-4 x^{2}+1)(2 x^{4}-4 x^{2}-1) \)
Given:
\( (2 x^{4}-4 x^{2}+1)(2 x^{4}-4 x^{2}-1) \)
To do:
We have to simplify the given product.
Solution:
We know that,
$(a+b)^2=a^2+b^2+2ab$
$(a-b)^2=a^2+b^2-2ab$
$(a+b)(a-b)=a^2-b^2$
Therefore,
$(2 x^{4}-4 x^{2}+1)(2 x^{4}-4 x^{2}-1)=[(2 x^{4}-4 x^{2})+1][(2 x^{4}-4 x^{2})-1]$
$=(2 x^{4}-4 x^{2})^{2}-(1)^{2}$
$=(2 x^{4})^{2}-2 \times 2 x^{4} \times 4 x^{2}+(4 x^{2})^{2}-1$
$=4 x^{8}-16 x^{6}+16 x^{4}-1$
Hence, $(2 x^{4}-4 x^{2}+1)(2 x^{4}-4 x^{2}-1)=4 x^{8}-16 x^{6}+16 x^{4}-1$.
Advertisements