Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Barber Lambert. in the United States
Mar 07,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( 2011^2 - 2010^2 = 4021 \)
Solución
We start with the expression:
\[
2011^2 - 2010^2
\]
This is a difference of two squares. Recall the algebraic identity:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Here, let \(a = 2011\) and \(b = 2010\). Substituting these into the identity gives:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Now, calculate the two factors:
1. \(2011 + 2010 = 4021\)
2. \(2011 - 2010 = 1\)
Multiplying these together:
\[
4021 \times 1 = 4021
\]
Thus, the final answer is:
\[
\boxed{4021}
\]
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Simplifique esta solución Extra Insights
To solve \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Calculating: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] This simplifies further: \[ = 1 \times (2011 + 2010) = 1 \times 4021 = 4021 \] Thus, \( 2011^2 - 2010^2 = 4021 \).
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