Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Bond Murphy. in the United States
Mar 10,2025
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. Let \( a = 2011 \) and \( b = 2010 \).
3. Substitute the values into the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
4. Compute the subtraction and addition:
\[
2011 - 2010 = 1 \quad \text{and} \quad 2011 + 2010 = 4021
\]
5. Multiply the results:
\[
1 \times 4021 = 4021
\]
\[
\textbf{Answer: } 4021
\]
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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 \( b = 2010 \). So: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the two expressions: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the result is \( \boxed{4021} \).
