$$ \text{Find } 2011^2 - 2010^2 \text{?} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:
$$
2011^2 - 2010^2
$$
This is a difference of squares. Recall the formula:
$$
a^2 - b^2 = (a+b)(a-b)
$$
Here, let $$a = 2011$$ and $$b = 2010$$. Applying the formula, we have:
$$
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
$$
First, calculate $$2011 + 2010$$:
$$
2011 + 2010 = 4021
$$
Next, calculate $$2011 - 2010$$:
$$
2011 - 2010 = 1
$$
Now, multiplying the two results:
$$
(4021)(1) = 4021
$$
Thus,
$$
2011^2 - 2010^2 = 4021
$$
$$2011^2 - 2010^2 = 4021$$

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