question_answer

By how much is \[{{({{x}^{2}}-{{y}^{2}})}^{2}}\] less than \[{{x}^{4}}+8{{x}^{2}}{{y}^{2}}+{{y}^{4}}?\]

A) \[-12{{x}^{2}}{{y}^{2}}\]                            

B) \[10{{x}^{2}}{{y}^{2}}\]

C) \[-12xy\]                       

D) \[10xy\]

Correct Answer: B

Solution :

(b) One can also do it m the following conventional way: Mathematical Ingenuity tips However, if we do it by first bringing \[{{({{x}^{2}}-{{y}^{2}})}^{2}}\] in the form of \[{{x}^{4}}+8{{x}^{2}}{{y}^{2}}+{{y}^{4}}\] and then, mentally think as to what extra term is getting added or subtracted, it will help solve us many more problems of similar nature.