SOLUTION: How does x^2(-e^-x)+e^-x(2x) simplify down to xe^-x(2-x) Thanks for the help in advance

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Question 998455: How does x^2(-e^-x)+e^-x(2x) simplify down to xe^-x(2-x)
Thanks for the help in advance
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

How does x%5E2%28-e%5E%28-x%29%29%2Be%5E%28-x%29%282x%29 simplify down to xe%5E%28-x%29%282-x%29:


x%5E2%28-e%5E%28-x%29%29%2Be%5E%28-x%29%282x%29......first write e%5E%28-x%29 as 1%2F%28e%5Ex%29%29%0D%0A%0D%0A%7B%7B%7Bx%5E2%28-%281%2Fe%5Ex%29%29%2B%281%2Fe%5Ex%29%282x%29
= -%28x%5E2%2Fe%5Ex%29%2B%282x%2Fe%5Ex%29
= -%28x%5E2%2B2x%29%2Fe%5Ex
= %28-1%29%28x%5E2%2B2x%29%2Fe%5Ex
= %282x-x%5E2%29%2Fe%5Ex
=+%28x%282-x%29%29%281%2Fe%5Ex%29.........write 1%2Fe%5Ex as e%5E%28-x%29
= x%282-x%29%2Ae%5Ex%5E-1