I am a little confused with the term expand. the question is find each term: the fourth term in the expansion of (4y+X)^4

Question

I looked at pascals triangle is the answer -4X(-4y^3)
does the problem call for the renaming or rearranging of x and y?

Answer 1

ah ham you know Pascal's triangle so you know binomial theorem after all
now
call a = 4 y
call b = x
then
(a+b)^4 = a^4 + 4 a^3b + 6 a^2b^2 + 4 a b^3 + b^4
which is
256 y^4 + 256x +6 (4y)^2 x^2 etc