1. **State the problem:** We need to find the value of $y$ given the expression $y = (a + b)(a - b)$ 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 useful algebraic identity. 3. **Substitute the values:** Plug in $a = 7.5$ and $b = 2.5$ into the formula: $$y = (7.5)^2 - (2.5)^2$$ 4. **Calculate the squares:** $$y = 56.25 - 6.25$$ 5. **Subtract to find $y$:** $$y = 50$$ **Final answer:** $y = 50$