Chapter 11 - 11.5 - The Binomial Theorem - 11.5 Exercises - Page 813: 50

$a=180$

According to the Binomial Theorem, the 3rd, that is, the ($2+1$)th term of $(x-2y)^{10}$ is: $_{10}C_2(x)^{10-2}(-2y)^2=\frac{10!}{(10-2)!\times2!}(x)^8(4)y^2=(45)x^8(4)y^2=180x^8y^2$ $ax^8y^2=180x^8y^2$ $a=180$