A) \[6{{x}^{5}}-3{{x}^{4}}y-6{{x}^{3}}{{y}^{2}}-6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{4}}\]
B) \[6{{x}^{5}}+3{{x}^{4}}y+6{{x}^{3}}{{y}^{2}}-{{x}^{2}}y+3{{x}^{2}}{{y}^{3}}-{{y}^{3}}\]
C) \[6{{x}^{5}}-3{{x}^{4}}y+6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{5}}\]
D) \[6{{x}^{5}}+3{{x}^{4}}y-6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{5}}\]
Correct Answer: B
Solution :
\[(6{{x}^{3}}-y+3{{x}^{2}}y)\times ({{x}^{2}}+{{y}^{2}})\] \[={{x}^{2}}(6{{x}^{3}}+3{{x}^{2}}y-y)+{{y}^{2}}(6{{x}^{3}}+3{{x}^{2}}y-y)\] \[=6{{x}^{5}}+3{{x}^{4}}y-{{x}^{2}}y+6{{x}^{3}}{{y}^{2}}+3{{x}^{2}}{{y}^{3}}-{{y}^{3}}\]
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