Question

what is the coefficiant of (x^4)( y^3) iterm in the expansion of (x-2y)^7

Answer 1

Answer:

The coefficient of $x^{4}$$y^{3}$ is -280

Step-by-step explanation:

Solving the Binomial expansion using the Pascal's triangle, it would be observed that an expansion to the power of 7 can be solved using;

1  7  21  35  35  21  7  1

Thus;

$(x - 2y)^{7}$ = 1. $x^{7}$ + 7.$x^{6}$(-2y) + 21.$x^{5}$$(-2y)^{2}$ + 35.$x^{4}$$(-2y)^{3}$ + 35.$x^{3}$$(-2y)^{4}$ + 21.$x^{2}$$(-2y)^{5}$ + 7.x$(-2y)^{6}$ + $(-2y)^{7}$

        = $x^{7}$ -14$x^{6}$y +84$x^{5}$$y^{2}$ -280$x^{4}$$y^{3}$ + 560$x^{3}$$y^{4}$ - 672$x^{2}$$y^{5}$ + + 448x$y^{6}$ - 128$y^{7}$

Therefore, the coefficient of $x^{4}$$y^{3}$ is -280