The difference of two squares identity states that \( a^2 - b^2 = (a-b)(a+b) \). In a scenario where you need to find the product of two numbers \( (x + a)(x - a) \) and know the values of \( x \) and \( a \), you could set \( x \) as the average of the two numbers and \( a \) as half their difference. For example, if you want to calculate the product of 12 and 8, you could express them as \( (10 + 2)(10 - 2) \), thus using the difference of squares: \( 10^2 - 2^2 = 100 - 4 = 96 \).
In 1–2 sentences, describe a scenario in which you might need to use the difference of two squares identity
to find the product of two numbers. First describe the general mathematical conditions and explain how you
would find x and a. Then provide a specific, real-world scenario
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