A) \[{{a}^{4}}-{{a}^{2}}{{b}^{2}}-2a{{b}^{3}}-{{b}^{7}}\]
B) \[6{{a}^{2}}b-3ab+10a-25\]
C) \[5a-3{{a}^{2}}+6\]
D) \[6{{a}^{4}}-{{a}^{2}}-{{b}^{2}}+2a{{b}^{3}}\]
Correct Answer: A
Solution :
Product \[=({{a}^{2}}+ab+{{b}^{2}})\,({{a}^{2}}-ab-{{b}^{2}})\] \[={{a}^{2}}({{a}^{2}}-ab-{{b}^{2}})+ab\,({{a}^{2}}-ab-{{b}^{2}})\,+{{b}^{2}}\,({{a}^{2}}-ab-{{b}^{2}})\]\[={{a}^{4}}-{{a}^{3}}b-{{a}^{2}}{{b}^{2}}+{{a}^{3}}b-{{a}^{2}}{{b}^{2}}-a{{b}^{3}}+{{a}^{2}}{{b}^{2}}-a{{b}^{3}}-{{b}^{4}}\]\[={{a}^{4}}-{{a}^{2}}{{b}^{2}}-2a{{b}^{3}}-{{b}^{4}}\]
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