Question: 8. $$(3x + 2)(2x + 3)$$
1. **State the problem:** Expand and simplify the expression $$(3x + 2)(2x + 3)$$.
2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$(a + b)(c + d) = ac + ad + bc + bd$$.
3. **Apply the formula:**
$$ (3x + 2)(2x + 3) = 3x \cdot 2x + 3x \cdot 3 + 2 \cdot 2x + 2 \cdot 3 $$
4. **Calculate each term:**
$$ 3x \cdot 2x = 6x^2 $$
$$ 3x \cdot 3 = 9x $$
$$ 2 \cdot 2x = 4x $$
$$ 2 \cdot 3 = 6 $$
5. **Combine like terms:**
$$ 6x^2 + 9x + 4x + 6 = 6x^2 + (9x + 4x) + 6 = 6x^2 + 13x + 6 $$
6. **Final answer:**
$$ 6x^2 + 13x + 6 $$