Chapter 11 - 11.5 - The Binomial Theorem - 11.5 Exercises - Page 813: 52

$a=326592$

According to the Binomial Theorem, the 3rd, that is, the ($2+1$)th term of $(3x+4y)^8$ is: $_8C_2(3x)^{8-2}(4y)^2=\frac{8!}{(8-2)!\times2!}(3x)^6(16)y^2=(28)(729)x^6(16)y^2=326592x^6y^2$ $ax^6y^2=326592x^6y^2$ $a=326592$