Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Conner Savage. in South Africa
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(2011^2 - 2010^2 = 4021\)
Solution
**Step 1: Apply the Difference of Squares Formula**
We know that for any numbers \(a\) and \(b\),
\[
a^2 - b^2 = (a - b)(a + b)
\]
**Step 2: Substitute the Given Values**
Here, \(a = 2011\) and \(b = 2010\). Thus,
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
**Step 3: Compute the Differences and Sum**
Calculate the difference:
\[
2011 - 2010 = 1
\]
Calculate the sum:
\[
2011 + 2010 = 4021
\]
**Step 4: Multiply to Get the Final Answer**
Now, multiply these two results:
\[
1 \times 4021 = 4021
\]
Thus,
\[
2011^2 - 2010^2 = 4021
\]
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Simplify this solution Bonus Knowledge
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 \(b = 2010\). First, calculate \(a - b\) and \(a + b\): - \(a - b = 2011 - 2010 = 1\) - \(a + b = 2011 + 2010 = 4021\) Now, apply the difference of squares: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] Therefore, \(2011^2 - 2010^2 = 4021\).
