Yes, you have the correct final answer. However, let me explain a better way to expand the expression and simplify it step-by-step.
To expand ((w) - (1)/(4))^2, you can use the binomial theorem or simply multiply the binomial by itself. Let's go through it step-by-step:
Step 1: Apply the distributive property to the two terms inside the parentheses:
(w - (1)/(4)) * (w - (1)/(4))
Step 2: Use the FOIL method to multiply the terms:
(w * w) + (w * (-1)/(4)) + ((-1)/(4) * w) + ((-1)/(4) * (-1)/(4))
Step 3: Simplify each multiplication:
w^2 - (1)/(4)w - (1)/(4)w + (1)/(16)
Step 4: Combine like terms:
w^2 - (1)/(2)w + (1)/(16)
So, the final answer is indeed w^2 - (1)/(2)w + (1)/(16).
Remember to always double-check your calculations and simplify fractions whenever possible.