Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Mcfarlane Wang. in South Africa
Jan 24,2025
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:
\[
a^2 - b^2 = (a - b)(a + b)
\]
**Step 1:** Identify \( a \) and \( b \).
\[
a = 2011 \\
b = 2010
\]
**Step 2:** Apply the difference of squares formula.
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
**Step 3:** Calculate the expressions inside the parentheses.
\[
2011 - 2010 = 1 \\
2011 + 2010 = 4021
\]
**Step 4:** Multiply the results.
\[
(1)(4021) = 4021
\]
**Conclusion:**
\[
2011^2 - 2010^2 = 4021
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
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 we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting these values back into the equation gives: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is \[ \boxed{4021} \]
