Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Kelly Stuart. in India
Feb 27,2025
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.
Calculating the two factors:
2011 - 2010 = 1
2011 + 2010 = 4021
Thus:
2011² - 2010² = 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 The Deep Dive
To simplify the expression \(2011^2 - 2010^2\), you can use the difference of squares formula, which states that \(a^2 - b^2 = (a-b)(a+b)\). Here, \(a = 2011\) and \(b = 2010\). Calculating the two parts: 1. \(a - b = 2011 - 2010 = 1\) 2. \(a + b = 2011 + 2010 = 4021\) Now, apply the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] So, \(2011^2 - 2010^2 = 4021\).
