Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by French Bond. in South Africa
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( 2011^2 - 2010^2 = 4021 \)
Solución
To find the value of \( 2011^2 - 2010^2 \), you can use the **difference of squares** formula:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Let's apply this formula to the given numbers:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Calculate the sums and differences inside the parentheses:
\[
2011 + 2010 = 4021
\]
\[
2011 - 2010 = 1
\]
Now, multiply these results together:
\[
4021 \times 1 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
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To find \( 2011^2 - 2010^2 \), you can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the terms: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, plug these values into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the result is \( 4021 \).
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