Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Warner Chavez. in South Africa
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
We use the difference of squares identity:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Letting \( a = 2011 \) and \( b = 2010 \), we have:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculate the difference:
\[
2011 - 2010 = 1
\]
Calculate the sum:
\[
2011 + 2010 = 4021
\]
Thus, the expression simplifies to:
\[
1 \times 4021 = 4021
\]
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Simplify this solution The Deep Dive
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, \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the two parts: 1. \(2011 - 2010 = 1\) 2. \(2011 + 2010 = 4021\) Now, substituting these values back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is \(4021\).
