Polynomial Subtraction help

Question

(2x-3x^2+9)-(5+x^2-8x)

 

As a part of the answer, I keep getting -6x instead of 10x. How do I get 10x into my answer. Please explain. The answer I get is:

 

-6x+(-4x^2)+4

 

I know this is incorrect.

Answer 1

Unless there is some special reason (like later substitution or later factoring or completing the square or ...), such expressions are written with descending powers of x (and this makes addition and subtraction simpler):

               -3x^3  +  2x  + 9

           - [  x^2    - 8x   + 5 ]        (to subtract, we will change all signs and add)

 

That is:

               -3x^3  +  2x   + 9

                -x^2   +  8x    - 5           (remember, there is 'subtract' and there is add 'negative')

              ----------------------

                -4x^2  + 10x  + 4          (note: 2 is a factor of all terms -- we made use that info. later)

Answer 2

Written explictly it is 2x-3x^2+9-5-x^2+8x or -4x^2+10x+4. Note -(-8x)=8x and 2x the first term give 10x. One has to be very careful with signs. I always have trouble with it even after over forty years.