SOLUTION: Can u help me factorise this 2^3x+2y + 2^4+y.3-2^y - 6

Since there are no parentheses, and it doesn't factorise as you
wrote it, it is impossible to tell what you meant to be part 
of an exponent and what is not part of an exponent.  If you
post again be sure to put in parentheses because you can't type 
exponents as superscripts.

I'll just take a wild guess that you meant this:

2^(3x+2y) + 2^(4+y*3)-2^(y-6)

which means this:



Then factorise out 



Explanation of the exponents in the parentheses:

The first exponent 3x+y+6 came from subtracting 
(3x+2y)-(y-6) which equals 3x+2y-y+6 or 3x+y+6

The second exponent 2y+10 came from subtracting 
(4+y*3)-(y-6) which equals 4+3y-y+6 or 2y+10.

Edwin

I'm thinking the x on the first term may have been a typo
and you meant this:

23+2y + 24+y∙3 - 2y - 6

If so then out of the first two terms,
factorise out the smaller power of 2 factor, 
which is 24+y by subtracting the
exponents:  24+y(2(3+2y)-(4+y)+3) = 24+y(23+2y-4-y+3) = 24+y(2y-1+3) 

24+y(2y-1+3) - 2y - 6
  
Out of the last two terms factorize out -2 which is the same
as 21.  We do this also by subtracting exponents:
-2y-6 = -21(2y-1+3) = -2(2y-1+3).
Now we have:

24+y(2y-1+3) - 2(2y-1+3).

Now there is a common factor of (2y-1+3).
Factorizing it out on the right, we have:

(24+y - 2)(2y-1+3)

Finally we can factorize out 2 from the first parentheses
by subtracting exponents: 21(24+y-1 - 1) = 21(23+y - 1) = 2(23+y - 1)  

2(23+y - 1)(2y-1+3)


Edwin