Question
2011^2 - 2010^2=
Ask by Peters Colon.
Mar 22,2025 16:08
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
We start with the difference of squares formula:
\[
a^2 - b^2 = (a+b)(a-b)
\]
Setting \( a = 2011 \) and \( b = 2010 \), we have:
\[
2011^2 - 2010^2 = (2011+2010)(2011-2010)
\]
Calculate each term:
\[
2011 + 2010 = 4021
\]
\[
2011 - 2010 = 1
\]
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 utilize the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \).
Here, let \( a = 2011 \) and \( b = 2010 \). Thus, we have:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculating the expressions in the parentheses:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
Now, substituting these values back into our equation:
\[
2011^2 - 2010^2 = 1 \times 4021 = 4021
\]
So, the answer is:
\[
\boxed{4021}
\]
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