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 \( (10 - 8)(10 + 8) = 2 \times 18 = 36 \).
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