Answer: [tex]e^x (x- e^{x})[/tex]
Step-by-step explanation:
The given expression is [tex]xe^x - e^{2x}[/tex]
We can write [tex]e^{2x}[/tex] as [tex]e^{x+x} = e^x \cdot e^x[/tex]
[[tex]\because a^{m+n}=a^m\cdot a^n[/tex]] → Property of exponents
Now , the the given expression [tex]xe^x - e^{x+x}[/tex] will become [tex]xe^x - e^{x}\cdot e^x[/tex]
Taking [tex]e^x[/tex] out as common (Greatest common factor) , we get
[tex]e^x (x- e^{x})[/tex] → Required factor form.
Hence, the answer is [tex]e^x (x- e^{x})[/tex].
