You should use binomial expansion `(a+b)^2 = a^2 + 2ab + b^2` , hence you should substitute 2x for a and 2 for b such that:

`(2x+2)^2 = (2x)^2 + 2(2x)2 + 2^2`

`(2x+2)^2 = 4x^2 + 8x + 4`

Hence, using binomial expansion yields`(2x+2)^2 = 4x^2 + 8x + 4` .

You may also write the square of binomial `2x + 2`  as the product:

`(2x + 2)(2x + 2)`

Factoring out 2 in each brackets yields:

`2(x+1)*2(x+1) = 4(x+1)(x+1)`

Opening the brackets yields:

`4(x+1)(x+1) = 4(x^2 + x + x + 1)` 

`4(x+1)(x+1) = 4x^2 + 4x + 4x + 4`

Collecting like terms yields:

4(x+1)(x+1) = 4x^2 + 8x + 4

Hence, expanding the binomial 2x + 2  by any methods yields `(2x+2)^2 = 4x^2 + 8x + 4` .