Determine the coefficient of x9y3 in the expansions of x 2y

Determine the coefficient of x^9y^3 in the expansions of (x + 2y)^12

(x + 2y)^12

The coefficient of anything in (a + b)^n is given by :

nCr * (a)^(n - r) * b^r

Here a = x and b = 2y and n = 12

12Cr * (x)^(12 - r) * (2y)^r

Now, since the exponent on y is 3, we know r = 3

So, 12C3 * x^(12 - 3) * (2y)^3

220 * x^9 * 8y^3

1760x^9y^3

So, the coefficient is : +1760 ---> ANSWER