Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Christensen Ellis. in Uganda
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
We can use the difference of squares formula:
\[
a^2 - b^2 = (a+b)(a-b)
\]
Let \( a = 2011 \) and \( b = 2010 \). Then:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Calculate each part:
\[
2011 + 2010 = 4021
\]
\[
2011 - 2010 = 1
\]
Thus:
\[
2011^2 - 2010^2 = 4021 \times 1 = 4021
\]
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Simplify this solution The Deep Dive
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 \( b = 2010 \). Then: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting back, we have: \[ 2011^2 - 2010^2 = 1 \cdot 4021 = 4021 \] So, the answer is \( 4021 \). And there you have it! Just a neat trick shows how powerful the difference of squares can be for quickly dealing with numbers!
