Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Montgomery Vega. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
We can use the difference of squares formula, \( a^2 - b^2 = (a-b)(a+b) \).
Let \( a = 2011 \) and \( b = 2010 \).
Step 1: Compute \( a - b \):
\[
2011 - 2010 = 1
\]
Step 2: Compute \( a + b \):
\[
2011 + 2010 = 4021
\]
Step 3: Multiply the results:
\[
(2011-2010)(2011+2010) = 1 \times 4021 = 4021
\]
Thus,
\[
2011^2 - 2010^2 = 4021.
\]
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Simplify this solution Bonus Knowledge
To solve \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Calculating: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Therefore, \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \cdot 4021 = 4021 \] So, the result is \( \boxed{4021} \).
