Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Smith Hardy. in South Africa
Feb 03,2025
Real Tutor 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. The difference of squares states that:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Calculate each part:
1. **Sum \( (a + b) \):**
\[
2011 + 2010 = 4021
\]
2. **Difference \( (a - b) \):**
\[
2011 - 2010 = 1
\]
Now, multiply the sum and the difference:
\[
4021 \times 1 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve \( 2011^2 - 2010^2 \), you can apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the parts: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now plug it back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is: \[ \boxed{4021} \]
