The correct option to use the difference of two squares identity for multiplying two numbers that are equidistant from another number is:
Option #1: Use the equation \(x^2 - a^2\), where \(a\) is the middle number (midpoint) and \(x\) is the distance from the midpoint to either endpoint.
This is because if the two numbers are equidistant from a midpoint \(a\), they can be expressed as \(a + d\) and \(a - d\) for some distance \(d\). The difference of squares identity states that:
\[ (a + d)(a - d) = a^2 - d^2 \]
In this case, \(x\) refers to \(d\) (the distance) and \(a\) refers to the midpoint. Thus \(x^2 - a^2\) represents the product of those two numbers.
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