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

Ask by Harmon Little. in South Africa
Feb 04,2025

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

Solución

To find \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula: \[ a^2 - b^2 = (a + b)(a - b) \] Let \( a = 2011 \) and \( b = 2010 \). Applying the formula: \[ 2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010) \] Calculate the sums and differences: \[ 2011 + 2010 = 4021 \] \[ 2011 - 2010 = 1 \] Now, multiply them together: \[ 4021 \times 1 = 4021 \] **Answer:** \( 4021 \)

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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 \( b = 2010 \). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times (2011 + 2010) = 1 \times 4021 = 4021. \] Thus, the result is \( \boxed{4021} \).

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