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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.

Simplify this equation: -1/2σ * ((x - μ)^2 - 2σ^2 * t * x)

This page explores the step-by-step simplification of a complex Gaussian expression involving parameters such as μ and σ. It simplifies a quadratic expression with terms like (x - μ)^2 and 2σ^2 * t * x. A detailed explanation is provided with mathematical concepts related to algebra and Gaussian functions. Suitable for advanced university students.

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