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How would you use the difference of two squares identity to multiply two numbers that are equidistant from another number? Ente...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.
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GPT-4o mini
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.
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.
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