Add the given algebraic expressions a-b+ab, b-c+bc, c-a+ac.

Hint: To solve this type of problem first we have to write all the given expressions in order. By adding write all the common terms and then canceling the terms with both negative and positive sign, leaves us with an expression which is the final answer.

Complete step-by-step solution -
Now writing all the terms,
\[a-b+ab,b-c+bc,c-a+ac\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
We know that if we add both positive terms and negative terms of the same value we get zero.
\[a-a=0\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Now adding all the expressions in (1) we get,
\[a-b+ab+b-c+bc+c-a+ac\]
Now further solving we get,
\[a+b+c-a-b-c+ab+bc+ca\]
Now further solving we get,
\[a-a+b-b+c-c+ab+bc+ca\]
Now applying (2) we get,
\[ab+bc+ca\].
After adding all the expressions we get,
\[ab+bc+ca\].

Note: This is a direct problem with simple addition and subtraction we can solve. Take care while canceling the terms. If values are given for a, b, c then substitute them after following all the above steps.