hi, i would really appreciate some help on simplifying this question:
-2(3e^-x-e^x)(-3e^-x-e^x)
could this be simplified as
-2(3e^-x-e^x)-(3e^-x-e^x)
which would then become
(-2-1)(3e^-x-e^x)
i feel this isn't right however...
To simplify the expression -2(3e^-x - e^x)(-3e^-x - e^x), you can follow the distributive property of multiplication over subtraction.
First, let's multiply the terms inside the parentheses:
-2 * 3e^-x = -6e^-x
-2 * -e^x = 2e^x
-3e^-x * -3e^-x = 9e^-2x
-3e^-x * -e^x = 3e^-x * e^x = 3e^0 = 3
(e^x * -3e^-x = -3e^0 = -3)
Now, substituting these values back into the expression, we have:
-6e^-x + 2e^x - 9e^-2x + 3
This is the simplified form of the expression -2(3e^-x - e^x)(-3e^-x - e^x).