Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Lane Mitchell. in South Africa
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is 4021.
Solution
We can simplify 2011² - 2010² using the difference of squares formula:
a² - b² = (a - b)(a + b)
Here, a = 2011 and b = 2010. Substituting these values gives:
2011² - 2010² = (2011 - 2010)(2011 + 2010)
= (1)(4021)
= 4021
So, the answer is 4021.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
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 \(b = 2010\). Calculating the two parts: - \(a - b = 2011 - 2010 = 1\) - \(a + b = 2011 + 2010 = 4021\) Now substituting back into the formula gives us: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Thus, the answer is \(4021\).
