Question

In Exercise,factor the expression. xex - e2x

Answer 1

Answer: $e^x (x- e^{x})$

Step-by-step explanation:

The given expression is $xe^x - e^{2x}$

We can write $e^{2x}$ as $e^{x+x} = e^x \cdot e^x$

[$\because a^{m+n}=a^m\cdot a^n$]  → Property of exponents

Now , the the given expression  $xe^x - e^{x+x}$  will become $xe^x - e^{x}\cdot e^x$

Taking $e^x$ out as common (Greatest common factor) , we get

$e^x (x- e^{x})$ → Required factor form.

Hence, the answer is $e^x (x- e^{x})$.