Question

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.

(2 points)

Answer 1

The difference of two squares identity states that \( a^2 - b^2 = (a - b)(a + b) \). To use this identity, you would identify two numbers \( a \) and \( b \) such that their squares differ by a known value, allowing you to find the product \( (a - b)(a + b) \).

For instance, if a local carpenter wants to calculate the area difference between two square tiles of size 10 cm and 8 cm, he can use the identity: the area of the larger tile is \( 10^2 = 100 \) cm² and the smaller tile is \( 8^2 = 64 \) cm², giving a difference of \( 100 - 64 = 36 \) cm², which can be expressed as \( (10 - 8)(10 + 8) = 2 \times 18 = 36 \).