What is the expansion of (x+2)^4?

This problem is straightforward if you take it step by step.

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

Step 1 is to begin with (x + 2) (x + 2). To do this, you multiply each of the elements from the first parenthesis times each of the items in the second. So, you get:

x * x = x^2

x * 2 = 2x

2 * x = 2x

2 * 2 = 4

Add these together, and you get x^2 + 4x + 4

Step 2 is to multiply all that first by x:

x^3 + 4x^2 + 4x

and then by 2:

2x^2 + 8x + 8.

Add them all together and you get: x^3 + 6 x^2 + 12x + 8.

Step 3 is to multiply all that by the last (x + 2).

First by x: x^4 + 6x^3 + 12x^2 + 8x

then by 2: 2x^3 + 12 x^2 + 24x +16

Add those two together and simplify for the final answer:

x^4 + 8x^3 + 24x^2 + 32x +16