Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Elliott Warren. in Nigeria
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 2011^2 - 2010^2 = 4021 \)
Solución
To find \( 2011^2 - 2010^2 \), 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:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
\[
= (4021)(1)
\]
\[
= 4021
\]
**Answer:** \( 4021 \)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
Did you know there's a nifty shortcut for finding the difference of squares? The difference \( a^2 - b^2 \) can be expressed as \( (a - b)(a + b) \). So for your problem, with \( a = 2011 \) and \( b = 2010 \), this means \( 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \cdot 4021 = 4021 \). Applying this method can save you time and effort, especially with larger numbers! Just remember that this principle works for any two numbers, making it a handy tool in your math toolkit. So, next time you come across a square difference, you can solve it in a snap!
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