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 states that \(a^2 - b^2 = (a - b)(a + b)\). To use this identity in a scenario, you would identify two numbers such that their squares are easily calculable, where \(x = a^2 - b^2\) with \(a\) and \(b\) representing convenient numbers that yield integers when squared.

For instance, if you need to find the product of \(48\) and \(32\) to determine the area of a rectangular garden where the sides are represented by these dimensions, you can express them as \(a = 40\) and \(b = 8\). Here, the identity gives \(48 \cdot 32 = (40^2 - 8^2) = (1600 - 64) = 1536\), thus simplifying the calculation.