Verified answer

You can use FOIL here. I won't explain it because that would take too long to type, but I'll include a link in the source (although you should just check your book).

√(5)*√(5) + √(5)*2 + (-2)*√(5) + (-2)*(2)

Simplify it now

5 + √(5)*2 - (2)*√(5) - 4 <------ Notice how the signs were used here. Always watch out for the negatives.

We can see that there's a positive √(5)*2 and then a negative √(5)*2, so those cancel.

Leaving us with 5 - 4, which = 1. :D

Identity Used : (a - b)(a + b) = (a² - b²)

Hence,

(√5-2)(√5+2) = { (√5)² - (2)² } = (5 - 4) = 1

a sum times the difference of the same two numbers is always the difference of the two squares

5 - 4 = 1

foil it

5+ 2root5 - 2root5 - 4

5-4

1

1.