Pregunta
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Potter Rodriquez. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( 2011^2 - 2010^2 = 4021 \)
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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Simplifique esta solución Extra Insights
To solve \(2011^2 - 2010^2\), we can use the algebraic identity for the difference of squares, which states that: \[ a^2 - b^2 = (a - b)(a + b) \] Here, let \(a = 2011\) and \(b = 2010\). Plugging in the values: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the terms in the parentheses: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting back into the equation: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the final answer is \[ \boxed{4021} \]
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