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

Ask by Hart Tucker. in Brazil
Feb 18,2025

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

Solución

Sabemos que a diferença de dois quadrados pode ser fatorada pela identidade:   a² - b² = (a - b)(a + b). Aplicando essa identidade em a = 2011 e b = 2010, temos:   2011² - 2010² = (2011 - 2010)(2011 + 2010). Calculando os termos:   2011 - 2010 = 1   2011 + 2010 = 4021 Portanto:   2011² - 2010² = 1 × 4021 = 4021.

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Para calcular \( 2011^2 - 2010^2 \), podemos usar a identidade da diferença de quadrados, que é \( a^2 - b^2 = (a - b)(a + b) \). Aqui, \( a = 2011 \) e \( b = 2010 \). Portanto, temos: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021. \] A resposta é \( 4021 \).

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