Verified answer

(2√2 +2)^2 = (2√2)^2 + 2(2√2)(2) + 2^2

= 8 + 8√2 + 4

= 12 + 8√2

I think you have asked a wrong question.

It should be to prove [(2√2 +2]^2 = 12 + 8√2. So

[(2√2 +2)]^2 = (2√2)^2 + 2^2 +2*(2√2)*2 = 8 + 4 + 8√2 = 12 + 8√2.

Show that (2√2 +2) = 12 + 8√2?

NOT possible. Because L.H.S. not = R.H.S.

AS

R.H.S = 12 + 8√2 = 4(3 + 2√2),

While

L.H.S. = (2√2 + 2)

SO something wrong in question.

(2√2+2)^2

4(2)+4√2+4√2+4

8+8√2+4

12+8√2

I hate to break it to you but that is not an equal statement. The left side (2√2 +2) is equal to 4.828 and the right side (12 + 8√2) is equal to 23.314. You can't show that two unequal expressions are equal.

isn't there something before "(2√2 +2)"? as it is, the equation is a contradiction.