Question: Expand and Simplify $(x+5)(x+6)$
1. **State the problem:** We need to expand and simplify the expression $$(x+5)(x+6)$$.
2. **Formula used:** To expand two binomials, we use the distributive property (also known as FOIL method for binomials):
$$ (a+b)(c+d) = ac + ad + bc + bd $$
3. **Apply the formula:**
$$ (x+5)(x+6) = x \cdot x + x \cdot 6 + 5 \cdot x + 5 \cdot 6 $$
4. **Calculate each term:**
$$ x \cdot x = x^2 $$
$$ x \cdot 6 = 6x $$
$$ 5 \cdot x = 5x $$
$$ 5 \cdot 6 = 30 $$
5. **Combine all terms:**
$$ x^2 + 6x + 5x + 30 $$
6. **Simplify by combining like terms:**
$$ x^2 + (6x + 5x) + 30 = x^2 + 11x + 30 $$
**Final answer:**
$$ x^2 + 11x + 30 $$