Laws of exponents for e^x

[riordo]

1. The problem statement, all variables and given/known data
Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x.

2. Relevant equations



3. The attempt at a solution

I've been guessing that you can combine the e^((-1/2)*x^2) components and thus end up with (x^2-1)x+e^((-1/2)*x^2)*x. Please let me know. Thanks.

[jeffreydk]

The most I can simplify it is just an exp term and a polynomial...

e^{-\frac{x^2}{2}}(-x^2+2x+1)

[HallsofIvy]

1. The problem statement, all variables and given/known data
Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x.

2. Relevant equations



3. The attempt at a solution

I've been guessing that you can combine the e^((-1/2)*x^2) components and thus end up with (x^2-1)x+e^((-1/2)*x^2)*x. Please let me know. Thanks.
Yes, you can factor out the e(-1/2)x^2x2 but you don't appear to have done it correctly! removing e(-1/2)x^2x2 from the first term leaves -(x2-1) and from the second leaves x. Removing it from both gives e(-1/2)x^2x2(-(x2-1+x)= -e-(1/2)x^2x2(x2- x+ 1).

[riordo]

Thank you. It appears that either you can combine the negative and positive e^((-1/2)*X^2) terms or eliminate the term by adding a negative value on both sides of the = sign. However that seems to me to make it more complicated. When I plug this into Mathematica software it simplifies to -e^((-1/2)*x^2)*x(x^2-3). I don't understand how it comes to this solution especially the (x^2-3). Let me know if you have any insight to what I am missing.
Thank you very much.

[riordo]

Solved. Thanks for the help.