To find the numerical equivalent of \( 81 \cdot 83 \), we can use the difference of squares formula, which states:
\[ a^2 - b^2 = (a - b)(a + b) \]
We can express \( 81 \) and \( 83 \) in relation to \( 82 \):
- \( 81 = 82 - 1 \)
- \( 83 = 82 + 1 \)
Now, we can apply the difference of squares:
\[ 81 \cdot 83 = (82 - 1)(82 + 1) = 82^2 - 1^2 \]
Calculating \( 82^2 \):
\[ 82^2 = 6724 \]
Now we can compute:
\[ 81 \cdot 83 = 6724 - 1 = 6723 \]
Thus, the correct numerical equivalent of \( 81 \cdot 83 \) is \( 6723 \).
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