A) \[\frac{3}{5}{{u}^{4}}v-{{u}^{3}}{{v}^{2}}-u{{v}^{4}}+\frac{3}{5}{{u}^{2}}{{v}^{3}}\]
B) \[\frac{{{u}^{4}}v}{5}-2u{{v}^{2}}\,+{{u}^{2}}{{v}^{3}}\,-\frac{5u{{v}^{4}}}{3}\]
C) \[\frac{3{{u}^{4}}v}{5}-4{{v}^{2}}+4{{u}^{2}}{{v}^{3}}-\frac{5u{{v}^{4}}}{3}\]
D) \[\frac{3{{u}^{4}}v}{5}-{{u}^{3}}{{v}^{2}}+{{u}^{2}}{{v}^{3}}-5u{{v}^{4}}\]
Correct Answer: A
Solution :
Product \[=(3{{u}^{2}}v-5u{{v}^{2}})\,\left( \frac{1}{5}{{u}^{2}}+\frac{1}{5}{{v}^{2}} \right)\] \[=3{{u}^{2}}v\,\left( \frac{1}{5}{{u}^{2}}+\frac{1}{5}{{v}^{2}} \right)\,-5u{{v}^{2}}\] \[\left( \frac{1}{5}\,{{u}^{2}}+\frac{1}{5}{{v}^{2}} \right)\] \[=\frac{3}{5}{{u}^{4}}v+\frac{3}{5}\,{{u}^{2}}{{v}^{3}}-{{u}^{3}}{{v}^{2}}-u{{v}^{4}}\]
You need to login to perform this action.
You will be redirected in
3 sec
