The expression $(a + b + c)^3$ can be expanded using the binomial theorem for three terms, also known as the trinomial expansion. The result is:

$(a + b + c)^3 = a^3 + b^3 + c^3 + 3a^2b + 3a^2c + 3b^2a + 3b^2c + 3c^2a + 3c^2b + 6abc$

Final Expanded Form:

$(a + b + c)^3 = a^3 + b^3 + c^3 + 3(a^2b + a^2c + b^2a + b^2c + c^2a + c^2b) + 6abc$

Would you like me to explain the steps behind this expansion or simplify further?

---

Related Questions:

1. How does the binomial theorem work for expansions like this?
2. What are the steps to generalize $(a + b + c)^n$ for higher powers?
3. How can this formula be applied to solve real-world problems?
4. Could you explain the symmetry of terms in the expansion?
5. How would this expansion differ if one or more terms were zero?

---

Tip:

Remember that coefficients in expansions like $(a + b + c)^3$ can also be derived using combinations from Pascal's triangle!