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

Ask by Hammond Crawford. in Nigeria
Feb 22,2025

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The answer is 4021.

Solución

We can use the difference of squares formula, which states:   a² - b² = (a + b)(a - b) Here, let a = 2011 and b = 2010. Then:   2011² - 2010² = (2011 + 2010)(2011 - 2010)           = (4021)(1)           = 4021 So, the answer is 4021.

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The Deep Dive

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 \(a - b\) gives: \[ 2011 - 2010 = 1 \] Calculating \(a + b\) gives: \[ 2011 + 2010 = 4021 \] Now, using the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] So, \(2011^2 - 2010^2 = 4021\).

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