1. **State the problem:** Expand and simplify the expression $$(4x - y)^2$$. 2. **Formula used:** The square of a binomial $$(a - b)^2$$ is given by the formula $$a^2 - 2ab + b^2$$. 3. **Apply the formula:** Here, $$a = 4x$$ and $$b = y$$. 4. **Calculate each term:** - $$a^2 = (4x)^2 = 16x^2$$ - $$-2ab = -2 \times 4x \times y = -8xy$$ - $$b^2 = y^2$$ 5. **Combine all terms:** $$16x^2 - 8xy + y^2$$ 6. **Final answer:** The expanded form of $$(4x - y)^2$$ is $$16x^2 - 8xy + y^2$$.