Step 1: Use the formula for the difference of squares, which states that a^2 - b^2 = (a + b)(a - b).

Given expression: 3a^2 - 6ab + 3b^2

Step 2: Factor out the common factor of 3:

3(a^2 - 2ab + b^2)

Step 3: Recognize that a^2 - 2ab + b^2 is the square of (a - b):

3(a - b)^2

Thus, the factored form of the expression 3a^2 - 6ab + 3b^2 is 3(a - b)^2.