(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

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(1+√3+√5)² - (√3+√5)² = ?

A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5


Nice question!
First recognize that (1+√3+√5)² - (√3+√5)² is a DIFFERENCE OF SQUARES.
Here are some examples of differences of squares:
x² - 25y²
4x² - 9y²
49m² - 100k²

In general, we can factor differences of squares as follows:
a² - b² = (a+b)(a-b)

So, (1+√3+√5)² - (√3+√5)² = [(1+√3+√5) + (√3+√5)][(1+√3+√5) - (√3+√5)]
= [1+2√3+2√5][1]
= 1+2√3+2√5

Answer:
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you can even do it with (A+B)^2 formula:

let √3+√5=x
Then the question becomes:
(1+x)^2-(x)^2=1^2+x^2+2x-x^2=1+2x=1+2(√3+√5)= option B
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