1. **State the problem:** Simplify the expression $$(2x-3)(2x-3)^2$$. 2. **Understand the expression:** The expression is a product of $(2x-3)$ and $(2x-3)^2$. Using the laws of exponents, when multiplying powers with the same base, we add the exponents. 3. **Apply the exponent rule:** $$ (2x-3)(2x-3)^2 = (2x-3)^{1+2} = (2x-3)^3 $$ 4. **Expand the cube:** To expand $(2x-3)^3$, use the binomial expansion formula: $$ (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 $$ where $a=2x$ and $b=3$. 5. **Calculate each term:** - $a^3 = (2x)^3 = 8x^3$ - $3a^2b = 3 \times (2x)^2 \times 3 = 3 \times 4x^2 \times 3 = 36x^2$ - $3ab^2 = 3 \times 2x \times 9 = 54x$ - $b^3 = 3^3 = 27$ 6. **Write the expanded form:** $$ (2x-3)^3 = 8x^3 - 36x^2 + 54x - 27 $$ **Final answer:** $$ (2x-3)(2x-3)^2 = (2x-3)^3 = 8x^3 - 36x^2 + 54x - 27 $$