In expansion of {left( {{x^2} - 2x} right)^{10}} , coefficient of {x^{16}} is

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7.Binomial Theorem

easy

In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is

A

$-1680$

B

$1680$

C

$3360$

D

$6720$

Solution

(c) The coefficient of ${x^{16}}$ in the expansion of ${({x^2} – 2x)^{10}}$

= The coefficient of ${x^{16}}$ in ${x^{10}}{(x – 2)^{10}}$

= The coefficient of ${x^6}$ in ${(x – 2)^{10}}$

= $^{10}{C_4}{.2^4},\,\,\,\,\left( {\,\,{T_{r + 1}} = {\,^n}{C_r}{x^{n – r}}{a^r}} \right)$

$ = 210 \times 16 $

$= 3360$.

Standard 11

Mathematics

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