Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Huff Pritchard. in South Africa
Jan 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
To find the value of \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Here, let:
- \( a = 2011 \)
- \( b = 2010 \)
Applying the formula:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Calculating the terms inside the parentheses:
\[
2011 + 2010 = 4021
\]
\[
2011 - 2010 = 1
\]
Now, multiply the results:
\[
4021 \times 1 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
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Simplify this solution Extra Insights
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 \( b = 2010 \): \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the first term: \[ 2011 - 2010 = 1 \] Calculating the second term: \[ 2011 + 2010 = 4021 \] Now, substitute these values back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the final answer is: \[ \boxed{4021} \]
