Binomial expansion of (x+2) ^4

The two terms are x and 2, thus, x+2 is a binomial. We have to multiply the binomial by itself four times since it is raised to 4th power.

Let us multiply x+2 by itself using Polynomial Multiplication:

(x+2) (x+2) = x^2 + 4x + 4

Taking the result, let us multiply it again by a+b:

(x^2 + 4x + 4) (x+2) = x^3 + 6x^2 + 12x + 8

And again:

(x^3 + 6x^2 + 12x + 8) (x+2) = x^4 + 8x^3 + 24x^2 + 32x + 16

The binomial expansion of (x+2) ^4 is x^4 + 8x^3 + 24x^2 + 32x + 16