What is the coefficient of \(x^2y^2\) in the expansion of \((x+y)^4+(x+2y)^4 \)?
(x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
(x + 2y)^4 = x^4 + 4x^3*2y + 6x^2*(2y)^2 + 4x*(2y)^3 + (2y)^4
So.....the sum of the x^2y^2 terms is
6x^2y^2 + 6x^2* (2y)^2 =
6x^2y^2 + 24x^2y^2 =
30
+471 
