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.
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.