1. **State the problem:** We are given the expression $y = (a + b)(a - b)$ and need to find the value of $y$ when $a = 7.5$ and $b = 2.5$. 2. **Recall the formula:** The expression $(a + b)(a - b)$ is a difference of squares, which simplifies to: $$y = a^2 - b^2$$ This is a key algebraic identity. 3. **Substitute the values:** Plug in $a = 7.5$ and $b = 2.5$: $$y = (7.5)^2 - (2.5)^2$$ 4. **Calculate the squares:** $$7.5^2 = 56.25$$ $$2.5^2 = 6.25$$ 5. **Subtract the squares:** $$y = 56.25 - 6.25 = 50$$ **Final answer:** $$\boxed{50}$$