1. **State the problem:** Expand and simplify the expression $$(2x + 5)(x - 2)(3x + 4)$$. 2. **Recall the formula:** To multiply multiple binomials or polynomials, multiply two at a time using the distributive property (FOIL for binomials), then multiply the result by the next polynomial. 3. **Step 1: Multiply the first two binomials:** $$(2x + 5)(x - 2) = 2x \cdot x + 2x \cdot (-2) + 5 \cdot x + 5 \cdot (-2)$$ $$= 2x^2 - 4x + 5x - 10$$ $$= 2x^2 + (\cancel{-4x} + \cancel{5x}) - 10 = 2x^2 + x - 10$$ 4. **Step 2: Multiply the result by the third binomial:** $$(2x^2 + x - 10)(3x + 4) = 2x^2 \cdot 3x + 2x^2 \cdot 4 + x \cdot 3x + x \cdot 4 - 10 \cdot 3x - 10 \cdot 4$$ $$= 6x^3 + 8x^2 + 3x^2 + 4x - 30x - 40$$ 5. **Step 3: Combine like terms:** $$6x^3 + (8x^2 + 3x^2) + (4x - 30x) - 40$$ $$= 6x^3 + 11x^2 - 26x - 40$$ **Final answer:** $$\boxed{6x^3 + 11x^2 - 26x - 40}$$