Question

What is the coeficcient of the x^4y^3 term in the expansion of (x-2y)^7?

Answer 1

Solution:

Given

$\begin{gathered} (x-2y)^7 \\ We\text{ want to determine the coefficient of x}^4y^3\text{ in the expansion} \end{gathered}$

The binomial expansion formula is given below

$\begin{gathered} To\text{ determine the coeffiecient of x}^4y^3,\text{ set k = 3} \\ n=7,\text{ } \\ The\text{ term that contain x}^4y^3,\text{ is }^7C_3(x)^{7-3}(-2y)^3 \end{gathered}$$\begin{gathered} =35x^4(-8)y^3 \\ =35(-8)\text{x}^4y^3 \\ =-280\text{x}^4y^3, \end{gathered}$$The\text{ coefficient of x}^4y^3\text{ is -280}$

The answer is -280