Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Matthews Coles. in Australia
Feb 03,2025
Real Tutor 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.
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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, \( a = 2011 \) and \( b = 2010 \). So we get: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part, we have: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, multiplying these results: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is \( 4021 \).
