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\[ \text{¿Cuál es } 2011^2 - 2010^2 \text{?} \]

Ask by Ward Barnett. in Argentina
Feb 19,2025

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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: \(4021\) La expresión \(2011^2 - 2010^2\) se simplifica a 4021.

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¿Sabías que esta pregunta puede resolverse de manera sorprendentemente sencilla utilizando la diferencia de cuadrados? Recuerda que \(a^2 - b^2 = (a - b)(a + b)\). En este caso, \(a = 2011\) y \(b = 2010\), lo que significa que \(2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)\). Así que la respuesta es \(1 \times 4021 = 4021\). Ese truco no solo se aplica a los números grandes, sino que es una técnica genial para simplificar cálculos en álgebra. Cada vez que veas una resta de cuadrados, puedes usar este método para encontrar respuestas más rápido, ya sea en tareas escolares o en la vida diaria, como calcular áreas o comparar precios. ¡Es un truco que definitivamente vale la pena tener en tu caja de herramientas matemáticas!

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