Question: Expand the following expression: $$(x - 6)^2$$
1. **State the problem:** We need to expand the binomial expression $$(x - 6)^2$$.
2. **Recall the formula for the square of a binomial:** $$(a - b)^2 = a^2 - 2ab + b^2$$.
3. **Apply the formula:** Here, $a = x$ and $b = 6$.
$$ (x - 6)^2 = x^2 - 2 \times x \times 6 + 6^2 $$
4. **Calculate each term:**
$$ x^2 - 12x + 36 $$
5. **Final expanded form:**
$$ x^2 - 12x + 36 $$
6. **Match with the given options:** This corresponds to option (a) $x^2 - 12x + 36$.
**Answer:** (a) $x^2 - 12x + 36$