Need help understanding multiplying radicals with variable inside ?

Question

Hi, please help me understand solving this I'm a little lost : 

 

(√2x+4 -1) (√2x+4 -1)

 

Note: The 4 is under the root but the 1 is not. 

Answer 1

I don't see (Z-1)(Z+1).  I see (Z-1)(Z-1) = Z² - 2Z + 1

 

(√2x+4 -1) (√2x+4 -1)

(2x + 4) -2 (√2x+4) + 1

2x + 5 -2 (√2x+4)

Answer 2

Look at the two expressions.  I assume that in each parenthesized grouping there appears

the square root of [2x+4], and following these there's a subtraction symbol in the first group, and an addition symbol in the second group.

 

So the structure (or pattern) of this is (Z-1)(Z+1) and of course this product is the famous DIFFERENCE OF SQUARES, i.e. Z²-1.

 

Therefore the product becomes (2x+4) - 1 = 2x +3 since Z² is the product of two identical radicals, thus the disappearance of the square root symbol.