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.

Question

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.

Answer 1

To multiply two numbers that are equidistant from another number using the difference of two squares identity, you would follow Option #1. The correct relationship is to set \( a \) as the middle number (midpoint) and \( x \) as the distance from the midpoint to either endpoint.

The equation would look like this: \((a - x)(a + x) = a^2 - x^2\).

Therefore, 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.