1. **State the problem:** Expand and fully simplify the expression $$(2x - 1)(x - 5)(x + 6)$$. 2. **Use the distributive property (FOIL for binomials) step-by-step:** First, multiply the first two binomials: $$ (2x - 1)(x - 5) = 2x \cdot x + 2x \cdot (-5) - 1 \cdot x - 1 \cdot (-5) $$ $$ = 2x^2 - 10x - x + 5 = 2x^2 - 11x + 5 $$ 3. **Now multiply the result by the third binomial $(x + 6)$:** $$ (2x^2 - 11x + 5)(x + 6) = 2x^2 \cdot x + 2x^2 \cdot 6 - 11x \cdot x - 11x \cdot 6 + 5 \cdot x + 5 \cdot 6 $$ $$ = 2x^3 + 12x^2 - 11x^2 - 66x + 5x + 30 $$ 4. **Combine like terms:** $$ 2x^3 + (12x^2 - 11x^2) + (-66x + 5x) + 30 = 2x^3 + x^2 - 61x + 30 $$ 5. **Final simplified expression:** $$ \boxed{2x^3 + x^2 - 61x + 30} $$ This is the fully expanded and simplified form of the original expression.