Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Malone Black. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
To find the value of \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Let \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
\[
= (1)(4021)
\]
\[
= 4021
\]
**Answer:** \( 4021 \)
Reviewed and approved by the UpStudy tutoring team
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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 \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Now, applying the formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the differences and sums: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now plug these values back into the equation: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] So, the final answer is \( \boxed{4021} \).
