Final answer:
To complete the square of the expression y^(2)-6y, add 9. The factored form of the expression is (y-3)^(2).
Step-by-step explanation:
To complete the square of the expression y^(2)-6y, we need to find the number that should be added. The number that should be added is half the coefficient of the linear term, squared. So in this case, the coefficient of the linear term is -6, half of which is -3, and -3 squared is 9. Therefore, we add 9 to complete the square to get y^(2)-6y+9.
To factor the expression, we can rewrite it as (y-3)^(2). So the factored form of the expression is (y-3)^(2).