Simplifying Equations with Exponential Terms

[riordo]

Homework Statement

Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x.

Homework Equations

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]

Homework Statement

Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x.

Homework Equations

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^2}x² but you don't appear to have done it correctly! removing e^{(-1/2)x^2}x² from the first term leaves -(x²-1) and from the second leaves x. Removing it from both gives e^{(-1/2)x^2}x²(-(x²-1+x)= -e^{-(1/2)x^2}x²(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.