A) \[\frac{-{{c}^{2}}(2b-c)}{{{a}^{3}}}\]
B) \[\frac{2b{{c}^{3}}}{{{a}^{2}}}\]
C) \[\frac{{{c}^{3}}{{b}^{3}}}{{{a}^{6}}}\]
D) \[\frac{{{b}^{2}}(2c+3a)}{{{a}^{3}}}\]
Correct Answer: A
Solution :
(a): \[{{\alpha }^{3}}{{\beta }^{3}}+{{\alpha }^{2}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{2}}={{(\alpha \beta )}^{3}}+{{\alpha }^{2}}{{\beta }^{2}}(\beta +\alpha )\] \[=\frac{{{c}^{3}}}{{{a}^{3}}}+\frac{{{c}^{2}}}{{{a}^{2}}}\left( \frac{-2b}{a} \right)=\frac{{{c}^{3}}-2b{{c}^{2}}}{{{a}^{3}}}=\frac{-{{c}^{2}}}{{{a}^{3}}}(2b-c)\]
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