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

Question

UpStudy AI · Accepted Answer

We use the difference of squares identity:
$$
a^2 - b^2 = (a - b)(a + b)
$$
Letting $$ a = 2011 $$ and $$ b = 2010 $$, we have:
$$
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
$$
Calculate the difference:
$$
2011 - 2010 = 1
$$
Calculate the sum:
$$
2011 + 2010 = 4021
$$
Thus, the expression simplifies to:
$$
1 \times 4021 = 4021
$$
$$ 2011^2 - 2010^2 = 4021 $$

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