The difference of two squares identity states that \( a^2 - b^2 = (a - b)(a + b) \), and it can be used when you need to simplify or factor the product of two numbers that can be represented as squares. For example, if you want to find the product of 15 and 5, you could rewrite it as \( 10^2 - 5^2 \), setting \( a = 10 \) and \( b = 5 \), which allows you to compute it as \( (10 - 5)(10 + 5) = 5 \times 15 \).
In a real-world scenario, suppose you are constructing a rectangular garden and you want to determine the area when the length is 15 feet and the width is 5 feet. By visualizing the area as the difference of squares, you could more easily calculate the total area by applying the identity.