Let $X$ and $\mu$ are $p$ dimensional vector and $\Sigma$ $p\times p$ dimensional matrix. I have to simplify the following expression.
$-\frac{1}{2}(X-\mu)^T\Sigma^{-1}(X-\mu)$
$=-\frac{1}{2}(X^T-\mu^T)\Sigma^{-1}(X-\mu)$
$=-\frac{1}{2}(X^T\Sigma^{-1}X-X^T\Sigma^{-1}\mu-\mu^T\Sigma^{-1}X+\mu^T\Sigma^{-1}\mu)$
But the result will be:
$-\frac{1}{2}(X-\mu)^T\Sigma^{-1}(X-\mu)=-\frac{1}{2}X^T\Sigma^{-1}X+X^T\Sigma^{-1}\mu-\frac{1}{2}\mu^T\Sigma^{-1}\mu.$