1. **State the problem:** Expand the expression $$(4a - b)^3$$. 2. **Formula used:** The cube of a binomial $$(x - y)^3$$ expands as $$x^3 - 3x^2y + 3xy^2 - y^3$$. 3. **Identify terms:** Here, $$x = 4a$$ and $$y = b$$. 4. **Apply the formula:** $$ (4a - b)^3 = (4a)^3 - 3(4a)^2(b) + 3(4a)(b)^2 - b^3 $$ 5. **Calculate each term:** - $$(4a)^3 = 64a^3$$ - $$3(4a)^2(b) = 3 imes 16a^2 imes b = 48a^2b$$ - $$3(4a)(b)^2 = 3 imes 4a imes b^2 = 12ab^2$$ - $$b^3 = b^3$$ 6. **Combine with signs:** $$ 64a^3 - 48a^2b + 12ab^2 - b^3 $$ 7. **Final answer:** $$(4a - b)^3 = 64a^3 - 48a^2b + 12ab^2 - b^3$$