Answer
$x^{10}-20x^9y+180x^8y^2$
Work Step by Step
Calculate the first three terms of $(x-2y)^{10}$ by using Binomial Theorem or Binomial expansion.
This implies $(x-2y)^{10}\\=\displaystyle \binom{10}{0}(x)^{10}(-2y)^0\\+\displaystyle \binom{10}{1}(x)^{9}(-2y)^1+\displaystyle \binom{10}{2})(x)^{8}(-2y)^2$
or, $=x^{10}+10x^9(-2y)+(45)x^8(4y^2)$
or, $=x^{10}-20x^9y+180x^8y^2$
