You use 25×80=2000 to estimate 23×82

We are given the base estimate:
$25 \times 80 = 2000$

We want to calculate $23 \times 82$. We can write 23 as $(25 - 2)$ and 82 as $(80 + 2)$.
So, $23 \times 82 = (25 - 2) \times (80 + 2)$

Using the distributive property (FOIL method), we expand the product:
$(25 - 2) \times (80 + 2) = (25 \times 80) + (25 \times 2) - (2 \times 80) - (2 \times 2)$

Now, substitute the values from our base estimate and the differences:
$25 \times 80 = 2000$
$25 \times 2 = 50$
$2 \times 80 = 160$
$2 \times 2 = 4$

Substitute these values back into the expanded expression:
$23 \times 82 = 2000 + 50 - 160 - 4$
$23 \times 82 = 2050 - 160 - 4$
$23 \times 82 = 1890 - 4$
$23 \times 82 = 1886$

The estimated value is 1886.