Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by May Tyler. in the Philippines
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 2011^2 - 2010^2 = 4021 \)
Solución
To find the value of \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculate each part:
1. **Difference**:
\[
2011 - 2010 = 1
\]
2. **Sum**:
\[
2011 + 2010 = 4021
\]
Now, multiply the two results:
\[
1 \times 4021 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To solve \(2011^2 - 2010^2\), you 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, applying the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] Thus, the value of \(2011^2 - 2010^2\) is \(\boxed{4021}\).
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