Question

Find the numerical equivalent of 81⋅83
.(1 point)
Responses

512
512

8^4


4,096
4,096

520

Answer 1

To find the numerical equivalent of \( 81 \cdot 83 \), we can use the difference of squares formula:

\[
a^2 - b^2 = (a-b)(a+b)
\]

In this case, we can set \( a = 82 \) (the average of 81 and 83) and \( b = 1 \) (the offset from the average):

\[
81 \cdot 83 = (82 - 1)(82 + 1) = 82^2 - 1^2
\]

Calculating \( 82^2 \):

\[
82^2 = 6724
\]
\[
1^2 = 1
\]

Now, substituting back:

\[
81 \cdot 83 = 6724 - 1 = 6723
\]

Thus, none of the provided responses (512, \( 8^4 \) which equals 4096, or 520) is correct for the product \( 81 \cdot 83 \). The correct calculation shows:

\[
81 \cdot 83 = 6723
\]