Final answer:
To make the expression w squared - 4w + ____ a perfect square, fill in the blank with 4, resulting in (w - 2)^2, which corresponds to answer option B.
Step-by-step explanation:
To make the expression w squared - 4w + ____ a perfect square, we need to fill in the blank with a number that allows the expression to be factored into the form (w - a)2. The general formula for a perfect square trinomial is (a - b)2 = a2 - 2ab + b2. In our case, a corresponds to w, and we already have the middle term, -4w, which represents -2ab. Thus, to find b2, we simply take the coefficient of w in the middle term, which is 4, and divide it by 2, giving us 2. Then we square 2 to get 4. So, the number we need to fill in the blank to make the expression a perfect square is 4, which corresponds to option B.