Question

How would you use the difference of two squares identity to multiply two numbers that are equidistant from another number? Enter the number of the correct option. Option #1: Use the equation x2−a2 , where a is the middle number (midpoint) and x is the distance from the midpoint to either endpoint. Option #2: Use the equation x2−a2 , where x is the middle number (midpoint) and a is the distance from the midpoint to either endpoint. Option #3: This operation is not possible without more information. (1 point) Option # is correct.

Answer 1

The correct option 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 you have two numbers that are equidistant from a midpoint \( a \), you can express them as \( a + d \) and \( a - d \), where \( d \) is the distance. The difference of squares identity states that:

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

Thus, Option #1 correctly describes how to apply the difference of squares identity in this scenario.