(simplify the expression (√3+2)²-√48+2√5•√5):

Firstly, let's expand the square of (√3 + 2):

(√3 + 2)² = (√3 + 2)(√3 + 2) = 3 + 4√3 + 4 (using the formula (a+b)² = a² + 2ab + b²)

Now, we substitute this back into the original expression:

(3 + 4√3 + 4) - √48 + 2√5•√5

Now simplify further:

4√3 + 7 - 4√4 + 10

√48 is simplified by breaking down 48 into √16•√3 = 4√3:

4√3 + 7 - 4•4 + 10

Which simplifies to:

4√3 + 7 - 16 + 10

Now combine like terms in the expression:

-9 + 14√3

Therefore, the simplified expression is:

-9 + 14√3