Question

find the coefficient of x^16 in (x^2-2x)^10​

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

As, we have to find the cofficient of $\sf{x^{16}}$ from equation $\sf{(x^2 - 2x)^{10}}$

So, Firstly we will factorise the polynomial.

$\sf{→ (x^2 - 2x)^{10}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{(a^x)^n = a^{x \times n}}}}}} \\ \\ \sf{(x^2)^{10}-(2x)^{10}} \\ \\ \sf{x^{20} - 1024x^{10}} \\ \\ \bf{Taking \: x^4 \: as \: common} \\ \\ \sf{x^4(x^{16} - 1024x^6)} \\ \\ \bf{\therefore \: cofficient \: of \: x^{16} \: is \: 1}$

$\Large{\red{\boxed{\blue{\boxed{\green{\boxed{\orange{\boxed{\pink{\boxed{\purple{\boxed{\gray{\boxed{\sf{\color{yellow}{Jai \: Shree \: Krishna}}}}}}}}}}}}}}}}}$