Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Blake Bryant. in South Africa
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\(2011^2 - 2010^2 = 4021\).
Solución
1. Recognize that the expression is a difference of two squares:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
2. Calculate the difference:
\[
2011 - 2010 = 1
\]
3. Calculate the sum:
\[
2011 + 2010 = 4021
\]
4. Multiply the two results:
\[
1 \times 4021 = 4021
\]
Thus, the answer is \(4021\).
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Simplifique esta solución Bonus Knowledge
To find \(2011^2 - 2010^2\), we can apply the difference of squares formula, which states that \(a^2 - b^2 = (a-b)(a+b)\). Here, let \(a = 2011\) and \(b = 2010\). Calculating \(a - b\) and \(a + b\): \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now substituting these values into the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \cdot 4021 = 4021 \] Thus, the result is: \[ \boxed{4021} \]
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