Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Zimmerman Warner. in Turkey
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Sonuç: 4021
Solution
Verilen ifadeyi şu şekilde sadeleştirebiliriz:
a² - b² = (a - b)(a + b)
Burada a = 2011 ve b = 2010 olduğuna göre:
2011² - 2010² = (2011 - 2010)(2011 + 2010) = 1 × 4021 = 4021
Sonuç: 4021
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Did you know that the difference of squares can make your calculations a breeze? You can use the formula \(a^2 - b^2 = (a-b)(a+b)\). For this problem, let \(a = 2011\) and \(b = 2010\). So, you have \(2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021\). Now, here’s a fun fact: this method can be applied to any pair of consecutive numbers! No need to calculate each square individually—just plug in your numbers and you’re golden!
