Questions: El término faltante para que se cumpla el producto (mn+2)^2= a) m^2 n^2 b) mn c) mn^2 d) m^2 n

El término faltante para que se cumpla el producto (mn+2)^2= a) m^2 n^2 b) mn c) mn^2 d) m^2 n
Transcript text: El término faltante para que se cumpla el producto $(m n+2)^{2}=$ a) $m^{2} n^{2}$ b) $m n$ c) $m n^{2}$ d) $m^{2} n$
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Solution

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Solution Steps

To find the missing term that completes the expression \((mn + 2)^2\), we need to expand the binomial and compare it to the given expression. The expanded form of \((mn + 2)^2\) will help us identify the missing term.

Step 1: Expansión del binomio

Expandimos el binomio \((mn + 2)^2\): \[ (mn + 2)^2 = m^2n^2 + 4mn + 4 \]

Step 2: Comparación con la expresión dada

La expresión dada es: \[ \square + 4m^2n^2 + 4 \] Comparando con la expansión, notamos que el término que falta es \(4mn\).

Step 3: Identificación del término faltante

Por lo tanto, el término que falta para que se cumpla el producto \((mn + 2)^2\) es \(4mn\).

Final Answer

La respuesta es \( \boxed{mn} \).

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