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\[ \text{Find } 2011^2 - 2010^2 \text{?} \]

Ask by Davey Rose. in Hong Kong
Feb 21,2025

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\( 2011^2 - 2010^2 = 4021 \)

Solución

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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Bonus Knowledge

To solve \( 2011^2 - 2010^2 \), we can use the difference of squares formula: \[ a^2 - b^2 = (a - b)(a + b). \] 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: \[ 2011^2 - 2010^2 = (1)(4021) = 4021. \] Thus, the answer is \( 4021 \).

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