1. **State the problem:** Simplify the expression $ (2x-1)(3x+2)^2 $. 2. **Recall the formula:** To simplify, first expand the square using the formula for a binomial square: $$ (a+b)^2 = a^2 + 2ab + b^2 $$ 3. **Apply the formula:** Here, $a = 3x$ and $b = 2$, so $$ (3x+2)^2 = (3x)^2 + 2 \cdot 3x \cdot 2 + 2^2 = 9x^2 + 12x + 4 $$ 4. **Rewrite the expression:** Now the original expression becomes $$ (2x-1)(9x^2 + 12x + 4) $$ 5. **Distribute:** Multiply each term in the first parenthesis by each term in the second: $$ 2x \cdot 9x^2 + 2x \cdot 12x + 2x \cdot 4 - 1 \cdot 9x^2 - 1 \cdot 12x - 1 \cdot 4 $$ 6. **Calculate each product:** $$ 18x^3 + 24x^2 + 8x - 9x^2 - 12x - 4 $$ 7. **Combine like terms:** $$ 18x^3 + (24x^2 - 9x^2) + (8x - 12x) - 4 = 18x^3 + 15x^2 - 4x - 4 $$ **Final answer:** $$ 18x^3 + 15x^2 - 4x - 4 $$