![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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
If $x = 3$ and $y = -1$, find the values of each of the following using in identity:$ \left(\frac{x}{4}-\frac{y}{3}\right)\left(\frac{x^{2}}{16}+\frac{x y}{12}+\frac{y^{2}}{9}\right) $
Given:
$x = 3$ and $y = -1$
To do:
We have to find the value of \( \left(\frac{x}{4}-\frac{y}{3}\right)\left(\frac{x^{2}}{16}+\frac{x y}{12}+\frac{y^{2}}{9}\right) \).
Solution:
We know that,
$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$
$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$
Therefore,
$(\frac{x}{4}-\frac{y}{3})(\frac{x^{2}}{16}+\frac{x y}{12}+\frac{y^{2}}{9})=(\frac{x}{4}-\frac{y}{3})[(\frac{x}{4})^{2}+\frac{x}{4} \times \frac{y}{3}+(\frac{y}{3})^{2}]$
$=(\frac{x}{4})^{3}-(\frac{y}{3})^{3}$
$=\frac{x^{3}}{64}-\frac{y^{3}}{27}$
$=\frac{(3)^{3}}{64}-\frac{(-1)^{3}}{27}$
$=\frac{27}{64}+\frac{1}{27}$
$=\frac{729+64}{1728}$
$=\frac{793}{1728}$
Hence, $(\frac{x}{4}-\frac{y}{3})(\frac{x^{2}}{16}+\frac{x y}{12}+\frac{y^{2}}{9})=\frac{793}{1728}$.
Advertisements