Binomial Theorem

Let the numerically greatest term in the expansion of (3x−16y)15 when x=‌

2

3

and y=‌

3

2

is Tr+1
Tr+1‌=‌15Cr(3(‌

2

3

))15−r(−16(‌

3

2

))r
‌=‌15Cr(2)15−r(−24)r
Clearly, the value the expression will be maximum only when the value r is largest possible even integer.
So, r=14‌‌[∵0≤r≤15 and r∈Z]
∴15 th term will be the numerically greatest term.