SOLUTION: if a-b=5 and ab=-1, what is the numerical value of (2a+3b-2ab)-(a+4b+ab)-(3ab+2b-2a)

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Question 52977: if a-b=5 and ab=-1, what is the numerical value of (2a+3b-2ab)-(a+4b+ab)-(3ab+2b-2a)
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
if a-b=5 and ab=-1, what is the numerical
value of 

(2a+3b-2ab)-(a+4b+ab)-(3ab+2b-2a)

Remove the parentheses:

2a+3b-2ab-a-4b-ab-3ab-2b+2a

Put like terms together:

2a-a+2a + 3b-4b-2b - 2ab-ab-3ab

Combine like terms:

3a - 3b -6ab

Factor 3 out of first two terms:

3(a - b) - 6ab

Substitute (5) for (a - b) and (-1) for ab 

3(5) - 6(-1)

15 + 6

21

That's the easy way.  

(The hard way would be to first solve the system

a - b =  5
   ab = -1

and then substitute.)

Edwin