(a + b)^2 = (a + b)•(a + b)

FOIL:

           ┌─F─┐ ┌─O─┐ ┌─I─┐ ┌─L─┐

          = a•a + a•b + b•a + b•b

           └─┬─┘ └────┬────┘ └─┬─┘

            a^2 +   2•a•b   + b^2

Given:

  (sqrt(3) + 2•sqrt(5))^2

  (sqrt(3) + 2•sqrt(5))•(sqrt(3) + 2•sqrt(5))

FOIL:

  ┌───────F───────┐ ┌───────O─────────┐ ┌─────────I───────┐ ┌─────────L─────────┐

 = sqrt(3)•sqrt(3) + sqrt(3)•2•sqrt(5) + 2•sqrt(5)•sqrt(3) + 2•sqrt(5)•2•sqrt(5)

  └───────┬───────┘ └──────────────────┬──────────────────┘ └─────────┬─────────┘

     sqrt(3)^2     +          4•sqrt(3)•sqrt(5)            + 2•2•sqrt(5)•sqrt(5)

     sqrt(3)^2     +          4•sqrt(3)•sqrt(5)            +     4•sqrt(5)^2

          3        +          4•sqrt(3)•sqrt(5)            +         4•5

          3        +          4•sqrt(3)•sqrt(5)            +          20

          23       +          4•sqrt(3)•sqrt(5)

                                    OR

          23       +             4•sqrt(15)