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The expression to develop is \((a + b + c)^2\). To expand this, we can use the distributive property (also known as the FOIL method for binomials), but in this case for three terms:

\[
(a + b + c)^2 = (a + b + c)(a + b + c)
\]

Expanding this step by step:

\[
(a + b + c)(a + b + c) = a(a + b + c) + b(a + b + c) + c(a + b + c)
\]

Now distribute each term:

1. \(a(a + b + c) = a^2 + ab + ac\)
2. \(b(a + b + c) = ab + b^2 + bc\)
3. \(c(a + b + c) = ac + bc + c^2\)

Now, sum all the terms:

\[
a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2
\]

Combine like terms:

\[
a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
\]

This matches option **b** in the multiple-choice answers:

\[
\boxed{b) \ a^2 + b^2 + c^2 + 2bc + 2ac + 2ab - 2abc}
\]

Do you need any further clarification or details?

Here are some related questions you might find useful:
1. How do you expand binomials like \((x + y)^2\)?
2. Can you explain how to expand \((x + y + z)^3\)?
3. What are the general formulas for expanding squares and cubes of sums?
4. How can we apply the distributive property for more complex polynomials?
5. Are there shortcut methods for squaring binomials or trinomials?

**Tip:** Always combine like terms carefully after expanding to avoid mistakes in the final expression!

Desarrollando la expresión (a + b + c)^2 se obtiene:

Learn how to expand the trinomial expression (a + b + c)^2 using the distributive property. This math problem covers key algebraic concepts and provides a detailed solution for high school students.

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