Determine the coefficient of

Question

wx^3y^2z^2 in (2w−x+y−2z)^8

Answer 1

Formula for Coefficients in a Trinomial Expansions is

\frac{n!}{r!}

n = power of the given expansion = 8

r = power of the asked coefficient

here it is asked for the coefficient of wx^{3}y^{2}z^{2}

their powers

w=1, x=3, y=2, z=2

so r = 1!* 3! * 2!* 2!

\Rightarrow\frac{8!}{1!* 3!*2!* 2!}

= 1680

\therefore coefficient of wx^{3}y^{2}z^{2} is 1680