A) \[{{x}^{3}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]
B) \[3{{x}^{2}}+5{{x}^{5}}{{y}^{2}}+3{{y}^{4}}\]
C) \[6{{x}^{2}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]
D) \[6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\]
Correct Answer: D
Solution :
(d): \[\left( 3{{x}^{2}}+{{y}^{2}} \right)\times \left( 2{{x}^{2}}+3{{y}^{2}} \right)\] \[=3{{x}^{2}}\left( 2{{x}^{2}}+3{{y}^{2}} \right)+{{y}^{2}}\left( 2{{x}^{2}}+3{{y}^{2}} \right)\] =\[6{{x}^{4}}+9{{x}^{2}}{{y}^{2}}+2{{x}^{2}}{{y}^{y}}+3{{y}^{4}}\] \[=6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\]
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