Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Murphy Simmons. in South Africa
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
1. Recognize the difference of squares formula:
\[
a^2 - b^2 = (a-b)(a+b)
\]
2. Set \( a = 2011 \) and \( b = 2010 \):
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
3. Compute the differences and sums:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
4. Multiply the results:
\[
1 \times 4021 = 4021
\]
So, the value of \( 2011^2 - 2010^2 \) is \( 4021 \).
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Simplify this solution Beyond the Answer
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Now substituting the values into the formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: \[ 2011 - 2010 = 1 \quad \text{and} \quad 2011 + 2010 = 4021 \] Now, substituting these back into the equation gives: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is: \[ \boxed{4021} \]
