Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Lowe Mejia. in India
Feb 20,2025
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.
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Simplify this solution Beyond the Answer
To solve the expression \( 2011^2 - 2010^2 \), 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, we can substitute these values back into the difference of squares formula: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Therefore, the answer is: \[ \boxed{4021} \]
