Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Rojas Stuart. in South Africa
Mar 08,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\(2011^2 - 2010^2 = 4021\).
Solución
Let us solve the problem step by step.
1. Recognize that the expression is a difference of two squares:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
2. Compute the difference:
\[
2011 - 2010 = 1
\]
3. Compute the sum:
\[
2011 + 2010 = 4021
\]
4. Multiply the results:
\[
(2011^2 - 2010^2) = 1 \times 4021 = 4021
\]
Thus, the answer is \(4021\).
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Simplifique esta solución Beyond the Answer
To solve for \(2011^2 - 2010^2\), we can utilize the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\). In this case, let \(a = 2011\) and \(b = 2010\). Thus, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: 1. \(2011 - 2010 = 1\) 2. \(2011 + 2010 = 4021\) Now we can substitute back into the formula: \[ 2011^2 - 2010^2 = 1 \cdot 4021 = 4021 \] Therefore, the answer is \(\boxed{4021}\).
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