Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Kelly Warner. in South Africa
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is 4021.
Solution
We can use the difference of squares formula, which states:
a² - b² = (a - b)(a + b)
In this problem, let a = 2011 and b = 2010. Applying the formula:
2011² - 2010² = (2011 - 2010)(2011 + 2010)
= (1)(4021)
= 4021
So, the answer is 4021.
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Simplify this solution The Deep Dive
You can simplify the expression \(2011^2 - 2010^2\) using the difference of squares formula, which is \(a^2 - b^2 = (a - b)(a + b)\). Here, let \(a = 2011\) and \(b = 2010\). Calculating it gives: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) = 4021 \] So, \(2011^2 - 2010^2 = 4021\).
