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(a^3+b^3)=(a+b)(a^2-ab+b^2) my question is why the -ab?

Mathematics
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Are you asking why the term "-ab" is in the middle of the formula?
Yes
And not a positive ab

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Other answers:

it cant be ab because the 1st term "a^2" does not have a "b". you can only take out if all the term got something in common.
it already factor in lowest term
@Hollywood_chrissy Maybe it would help you see it to multiply out the stuff on the right side of the equation. You end up with (a^2)(b) and (a)(b^2) terms, and by having "-ab", the signs on those terms alternate and ultimately all cancel out, leaving only the cubed terms. It is similar to when you factor a difference of squares... a^2 - b^2 = (a+b)(a-b) <<-- the signs in the factored version cause the unwanted terms like "ab" to cancel out, leaving only the squared terms.
Yeah, i just noticed that too.

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