48x²+72xy+27y²

First, observe that the expression can potentially be factored as a perfect square trinomial. To verify this, we want to match the expression to the form a^2 + 2ab + b^2:

1. Rewrite the original expression: 48x^2 + 72xy + 27y^2.

2. Factor out the common factor 3 from each term:
3(16x^2 + 24xy + 9y^2).

3. Recognize that the quadratic inside the parentheses can be factored:
16x^2 = (4x)^2,
9y^2 = (3y)^2,
24xy = 2(4x)(3y).

4. So the expression becomes:
3((4x + 3y)^2).

Therefore, the factorization is:

3(4x + 3y)^2

And the answer is:

3(4x + 3y)^2