Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Adkins Brooks. in South Africa
Mar 08,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( 2011^2 - 2010^2 = 4021 \)
Solución
1. Recognize the difference of squares formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
2. Identify \( a = 2011 \) and \( b = 2010 \).
3. Substitute into the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
4. Calculate the difference:
\[
2011 - 2010 = 1
\]
5. Calculate the sum:
\[
2011 + 2010 = 4021
\]
6. Multiply the results:
\[
1 \times 4021 = 4021
\]
Thus, the answer is:
\[
\boxed{4021}
\]
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Simplifique esta solución Beyond the Answer
To solve \(2011^2 - 2010^2\), we can apply the difference of squares formula, which is \(a^2 - b^2 = (a-b)(a+b)\). Here, let \(a = 2011\) and \(b = 2010\). Thus: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times (2011 + 2010) = 1 \times 4021 = 4021 \] So, \(2011^2 - 2010^2 = 4021\).
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