Precalculus, Chapter 9, 9.5, Section 9.5, Problem 27

You need to use the binomial formula, such that:
(x+y)^n = sum_(k=0)^n ((n),(k)) x^(n-k) y^k
You need to replace 2x for x, y for y and 3 for n, such that:
(2x+y)^3 = 3C0 (2x)^3+3C1 (2x)^2*(y)^1+3C2 (2x)^1*(y)^2+3C3(y)^3
By definition, nC0 = nCn = 1, hence 3C0 = 3C3 = 1.
By definition nC1 = nC(n-1) = n, hence 3C1 = 3C2 = 3.
(2x+y)^3 = 8x^3+12x^2*y+6x*y^2+y^3
Hence, expanding the complex number using binomial theorem yields the simplified result (2x+y)^3 = 8x^3+12x^2*y+6x*y^2+y^3.