Find the coefficient of x3 y4 in the expansion of ( x+2y )^7.

The coefficient of x³y⁴ in the expansion of ( x+2y)⁷ is 560.

Explanation:

The given expression is

According to binomial expansion,

The r+1th term of the expansion is

      ... (1)

In the term  x³y⁴ the power of x is 3 and the power of y is 4. It means the value of r is 4 and the value n-r is 3.

Put n=7 and r=4 in equation (1)

Therefore the coefficient of x³y⁴ in the expansion of ( x+2y)⁷ is 560.