The simplified form of the given equation is:

$\sigma t x - \frac{(x - \mu)^2}{2\sigma}$

Would you like more details on this simplification or have any further questions?

Here are five related questions for further exploration:

1. How would this expression change if $\mu = 0$?
2. Can you explain the significance of the parameters $\mu$ and $\sigma$ in a probability distribution?
3. How would you interpret this expression in the context of Gaussian functions?
4. What happens if we differentiate this equation with respect to $x$?
5. Can this expression be rewritten in terms of another variable?

Tip: When simplifying complex expressions, always check for common factors or patterns such as difference of squares or distributive properties.