Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Boone Brewer. in South Africa
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( 2011^2 - 2010^2 = 4021 \)
Solución
We start by recognizing the difference of squares formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Let \(a = 2011\) and \(b = 2010\). Then,
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
First, compute \(2011 - 2010\):
\[
2011 - 2010 = 1
\]
Next, compute \(2011 + 2010\):
\[
2011 + 2010 = 4021
\]
Now, multiply the two results:
\[
1 \times 4021 = 4021
\]
Thus, the answer is:
\[
4021
\]
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Simplifique esta solución Bonus Knowledge
Did you know that the difference of squares can be a quick math trick? Here, you can express \(2011^2 - 2010^2\) as \((2011 - 2010)(2011 + 2010)\). This simplification makes it easy to compute! So, let's calculate: \(2011 - 2010 = 1\) and \(2011 + 2010 = 4021\). Multiplying these gives you \(1 \times 4021 = 4021\). Voilà! The answer is 4021, and you’ve just used a nifty algebraic identity!
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