Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Wilson Hammond. in South Africa
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\(2011^2 - 2010^2 = 4021\).
Solución
Given the expression \(2011^2 - 2010^2\), we can use the difference of squares formula, which states:
\[
a^2 - b^2 = (a+b)(a-b)
\]
Let \(a = 2011\) and \(b = 2010\). Substituting these values, we have:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Now, compute the terms inside the parentheses:
\[
2011 + 2010 = 4021
\]
\[
2011 - 2010 = 1
\]
Thus, the expression becomes:
\[
2011^2 - 2010^2 = 4021 \times 1 = 4021
\]
So, the final answer is:
\[
\boxed{4021}
\]
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Simplifique esta solución Mind Expander
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, \( a = 2011 \) and \( b = 2010 \). Calculating \( a-b \) gives: \[ 2011 - 2010 = 1 \] Calculating \( a+b \) gives: \[ 2011 + 2010 = 4021 \] Now, substituting into the formula: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Therefore, \( 2011^2 - 2010^2 = 4021 \).
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