https://r2.erweima.ai/mathbot/image/172634879877798ubkl0k.jpg

The expression in your image is the sum:

\[
ab + ac + ba + bc + ca + cb
\]

This can be rewritten by regrouping terms:

\[
(ab + ba) + (ac + ca) + (bc + cb)
\]

Now, since \(ab = ba\), \(ac = ca\), and \(bc = cb\) (due to the commutative property of multiplication), we can simplify the expression:

\[
2ab + 2ac + 2bc
\]

Factor out the 2:

\[
2(ab + ac + bc)
\]

Therefore, the entire sum is always a multiple of 2.

### Answer:
The sum is always a multiple of **2**.

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Do you want more details or have any questions? Here are some related questions to consider:

1. How does the commutative property of multiplication affect simplifications like this one?
2. What other mathematical properties could simplify similar expressions?
3. What happens if the terms have more variables (e.g., terms like \( ab + cd \))?
4. How would this expression change if we included exponents?
5. Can you find a way to represent this expression geometrically?

**Tip:** In expressions with multiple terms, look for common factors and apply basic properties like commutative or distributive to simplify.

¿De qué número es siempre múltiplo la suma: ab + ac + ba + bc + ca + cb?

Descubre de qué número siempre es múltiplo la suma de términos ab + ac + ba + bc + ca + cb. Utilizando el concepto de la propiedad conmutativa de la multiplicación, simplificamos la expresión y demostramos que siempre es múltiplo de 2. Ideal para estudiantes de secundaria.

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