Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Savage Riley. in South Africa
Feb 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is 4021.
Solution
We can use the difference of squares formula:
a² - b² = (a + b)(a - b).
Here, a = 2011 and b = 2010, so:
2011² - 2010² = (2011 + 2010)(2011 - 2010) = (4021)(1) = 4021.
Thus, the answer is 4021.
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Simplify this solution Bonus Knowledge
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). In this case, let \( a = 2011 \) and \( b = 2010 \). Calculating the values: \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now we can apply the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] So, \( 2011^2 - 2010^2 = 4021 \).
