Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by King Mullins. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(2011^2 - 2010^2 = 4021\).
Solution
Using 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, calculate the difference:
\[
2011 - 2010 = 1
\]
Next, calculate the sum:
\[
2011 + 2010 = 4021
\]
Now, multiply the two results:
\[
1 \times 4021 = 4021
\]
Thus, the answer is \(4021\).
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Simplify this solution 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, 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 we apply the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Therefore, the result is \[ \boxed{4021} \]
