Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Pena Chadwick. in Mozambique
Mar 06,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
Calculate or simplify the expression \( 2011^2 - 2010^2 \).
Calculate the value by following steps:
- step0: Calculate:
\(2011^{2}-2010^{2}\)
- step1: Calculate:
\(\left(2011+2010\right)\left(2011-2010\right)\)
- step2: Calculate:
\(4021\times 1\)
- step3: Multiply the terms:
\(4021\)
The result of \(2011^2 - 2010^2\) is 4021.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
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 \(a - b\) and \(a + b\): \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now, substituting back into the difference of squares formula: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Thus, the answer is \[ \boxed{4021} \]
