1. Stating the problem: Simplify the expression $$(3r - 2s)(3r - 2s)(3r - 2s)$$ which is the cube of the binomial $3r - 2s$. 2. Recognize that this is equivalent to $$(3r - 2s)^3$$. 3. Use the binomial expansion formula for cubes: $$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$ where $a = 3r$ and $b = 2s$. 4. Calculate each term: - $a^3 = (3r)^3 = 27r^3$ - $3a^2b = 3 \times (3r)^2 \times 2s = 3 \times 9r^2 \times 2s = 54r^2s$ - $3ab^2 = 3 \times 3r \times (2s)^2 = 3 \times 3r \times 4s^2 = 36rs^2$ - $b^3 = (2s)^3 = 8s^3$ 5. Substitute back into the expansion: $$27r^3 - 54r^2s + 36rs^2 - 8s^3$$ 6. Final answer: $$(3r - 2s)^3 = 27r^3 - 54r^2s + 36rs^2 - 8s^3$$