Answer
$x^{9}-18x^8y+144x^7y^2$
Work Step by Step
Apply Binomial Theorem or Binomial expansion to find the first three terms of $(x-2y)^{9}$.
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Now, $(x-2y)^{9}=\displaystyle \binom{9}{0}x^{9}(-2y)^0+\displaystyle \binom{9}{1}x^{8}(-2y)^1+\displaystyle \binom{9}{2}x^{7}(-2y)^2$
$=(1)x^{9}(1)+9x^8(-2y)+36x^7(4y^2)$
Thus, $(x-2y)^{9}=x^{9}-18x^8y+144x^7y^2$
