(t-3)(t+5)

To expand the expression \((t - 3)(t + 5)\), you can use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms: \[ t \cdot t = t^2 \]

2. Outer: Multiply the outer terms: \[ t \cdot 5 = 5t \]

3. Inner: Multiply the inner terms: \[ -3 \cdot t = -3t \]

4. Last: Multiply the last terms: \[ -3 \cdot 5 = -15 \]

Now combine all these results: \[ t^2 + 5t - 3t - 15 \]

Combine like terms: \[ t^2 + (5t - 3t) - 15 = t^2 + 2t - 15 \]

So, the expanded form of \((t - 3)(t + 5)\) is: \[ t^2 + 2t - 15 \]