Question
If (x - 4)(x2 + 4x + 16) = x3 - p, then p is equal to?
Answer: Option C
$$\eqalign{
& {\text{We know that }} \cr
& {a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right) \cr
& {x^3} - p = \left( {x - 4} \right)\left( {{x^2} + 4x + 16} \right) \cr
& \Rightarrow {x^3} - p = \left( {{x^3} - {4^3}} \right) \cr
& \Rightarrow p = {4^3}{\text{ }}\left( {{\text{By comparison}}} \right) \cr
& {\text{So, }}p = 64 \cr} $$
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$$\eqalign{
& {\text{We know that }} \cr
& {a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right) \cr
& {x^3} - p = \left( {x - 4} \right)\left( {{x^2} + 4x + 16} \right) \cr
& \Rightarrow {x^3} - p = \left( {{x^3} - {4^3}} \right) \cr
& \Rightarrow p = {4^3}{\text{ }}\left( {{\text{By comparison}}} \right) \cr
& {\text{So, }}p = 64 \cr} $$
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