To find: the coefficient of x⁷y² in the expansion of (x + 2y)⁹

Formula Used:

A general term, T_r+1 of binomial expansionis given by,

T_r+1 ⁿC_r x^n-r y^r where

ⁿC_r

Now, finding the general term of the expression, (x + 2y)⁹, we get

T_r+1⁹C_r

The value of r for which coefficient of x⁷y² is defined

r=2

Hence, the coefficient of x⁷y² in the expansion of (x + 2y)⁹ is given by:

T₃⁹C₃

T₃⁹C₃

T₃

T₃

T₃=336

Thus, the coefficient of x⁷y² in the expansion of (x + 2y)⁹ is 336