Write down and simplify, the first $3$ terms in the expansion of ${{\left( 2-p \right)}^{7}}$ in

Question

Write down and simplify, the first $3$ terms in the expansion of ${{\left( 2-p \right)}^{7}}$ in ascending powers of $p$. [2] Find the value of $n$ where $n$ is a positive integer, given that the coefficient of ${{x}^{2}}$ is $96$ in the expansion of ${{\left( 1+x \right)}^{n}}{{\left( 2-x+{{x}^{2}} \right)}^{7}}$.[4]

Accepted Answer

(i) $128-448p+672p^2+\cdots$ (ii) $n=4$

2016 TKGS AM P1 Q4

2016 TKGS AM P1 Q4

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