SOLUTION: (a)(b)+(-a)(b)+(b)(-a)-(a)(b)-(-a)(-b) How do I solve this or what is the answer?

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Question 737121: (a)(b)+(-a)(b)+(b)(-a)-(a)(b)-(-a)(-b)
How do I solve this or what is the answer?

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
-c is another way of expressing %28-1%29%2Ac.
A basic law of real numbers is c%2B%28-c%29=0.

For two real numbers a and b, a-b means the same thing as a+ (-b).

Review those facts for a few minutes and try.... understand them.

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, can you see how?
=ab%2B%28-ab%29%2B%28-ab%29%2B%28-ab%29%2B%28-ab%29, but do you know why I show it this way?
=.
=-3ab, Excuse me for skipping a step or two.

post-note: There are a couple of ways to go from the step just before the "=." line. The more pathways are shown, the more confusing a solution can be for a student. What may be best if a step is missing is for the student to try to fill in any missing steps. Knowing exactly which steps a student needs and which would be distracting is often not possible. Direct interaction is a better situation sometimes than sending and reading text & symbols messages.
One suggestion for the step at the "=." line is to use the additive inverse concept, like for some number c, we can be assured of c+(-c)=0. The number, c, may stand for any real number, like r, or uw, or xwp, or ab...