Question: Return the original user prompt in the "prompt" field. Wrap every mathematical expression, number used in a calculation, equation, fraction, variable, or formula in $...$ for inline math or $$...$$ for display math.
User: (p - 2) \cdot (p - 2) \cdot (p - 2)
1. **State the problem:** Simplify the expression $$ (p - 2) \cdot (p - 2) \cdot (p - 2) $$.
2. **Formula used:** This is the cube of a binomial, which can be written as $$ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 $$.
3. **Apply the formula:** Here, $$ a = p $$ and $$ b = 2 $$.
4. **Calculate each term:**
$$ a^3 = p^3 $$
$$ 3a^2b = 3 \cdot p^2 \cdot 2 = 6p^2 $$
$$ 3ab^2 = 3 \cdot p \cdot 2^2 = 3 \cdot p \cdot 4 = 12p $$
$$ b^3 = 2^3 = 8 $$
5. **Write the expanded form:**
$$ (p - 2)^3 = p^3 - 6p^2 + 12p - 8 $$
6. **Final answer:**
$$ \boxed{p^3 - 6p^2 + 12p - 8} $$