Asked by e
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)
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GPT-4o mini
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.
**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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