Question: Perform the multiplication and combine like terms
$$(3x-5)(x+2)(x+1)$$
Options:
$3x^3+2x^2+9x+10$
$3x^3+2x^2-11x-10$
$3x^3+4x^2+11x+10$
$3x^3+4x^2-9x-10$
1. **State the problem:** Multiply and simplify the expression $$(3x-5)(x+2)(x+1)$$.
2. **Use the distributive property:** First multiply the last two binomials:
$$ (x+2)(x+1) = x\cdot x + x\cdot 1 + 2\cdot x + 2\cdot 1 = x^2 + x + 2x + 2 = x^2 + 3x + 2 $$
3. **Rewrite the expression:**
$$ (3x-5)(x^2 + 3x + 2) $$
4. **Distribute $(3x-5)$ over the trinomial:**
$$ 3x(x^2 + 3x + 2) - 5(x^2 + 3x + 2) $$
5. **Multiply each term:**
$$ 3x \cdot x^2 = 3x^3 $$
$$ 3x \cdot 3x = 9x^2 $$
$$ 3x \cdot 2 = 6x $$
$$ -5 \cdot x^2 = -5x^2 $$
$$ -5 \cdot 3x = -15x $$
$$ -5 \cdot 2 = -10 $$
6. **Combine like terms:**
$$ 3x^3 + (9x^2 - 5x^2) + (6x - 15x) - 10 = 3x^3 + 4x^2 - 9x - 10 $$
7. **Final answer:**
$$ \boxed{3x^3 + 4x^2 - 9x - 10} $$