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If $1 + x^{4} + x^{5} = \sum_{i = 0}^{5} a_{i} {(1 + x)}^{i}$ for all $x \in R$ then $a_{2}$ is equal to

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$- 8$

$6$

$- 4$

$10$

answer is A.

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Detailed Solution

Put 1+x=y, we get $1 + {(y - 1)}^{4} + {(y - 1)}^{5} = \sum_{i = 0}^{5} a_{i} y^{i}$

Equating coefficients of $y^{2}$ on both sides, we get $a_{2} =^{4} C_{2} -^{5} C_{3} = 6 - 10 = - 4$

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