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.

Answer 1

The difference of two squares identity applies when you have two numbers in the form \( (a + x)(a - x) \), which can be simplified to \( a^2 - x^2 \), where \( a \) is the average of the two numbers and \( x \) is half the difference between them. For instance, if you need to multiply 48 and 52, you could set \( a = 50 \) (the midpoint) and \( x = 2 \) (half the difference), allowing you to calculate their product as \( 50^2 - 2^2 = 2500 - 4 = 2496 \).

In a real-world scenario, consider a company that produces two different sizes of a product, measuring 48 units and 52 units; they wish to find the total area represented by both dimensions in their inventory quickly without multiplying directly.