Question

Add the following:
a-b+ab, b-c+bc, c-a+ac.

Answer 1

Hint: In this question we simply need to add the three given entities, use the concept that only likewise terms get added or subtracted. Marking the entities into 3 equations and then adding them in horizontal manner helps in easy simplification.

Complete step-by-step answer:
Given expressions are
$\left( {a - b + ab} \right)$……………………… (1)
$\left( {b - c + bc} \right)$………………………. (2)
$\left( {c - a + ac} \right)$………………………… (3)
 Now we have to add these equations.
So add equation (1), (2) and (3) we have,
$ \Rightarrow \left( {a - b + ab} \right) + \left( {b - c + bc} \right) + \left( {c - a + ac} \right)$
Now collect like terms we have,
$ \Rightarrow \left( {1 - 1} \right)a + \left( { - 1 + 1} \right)b + \left( { - 1 + 1} \right)c + ab + bc + ca$
Now as we see +1 and -1 are cancel out and gives us 0 so the remaining terms are,
 \[ \Rightarrow \left( 0 \right)a + \left( 0 \right)b + \left( 0 \right)c + ab + bc + ca\]
Now as we know 0 multiplied by something is also zero.
\[ \Rightarrow 0 + 0 + 0 + ab + bc + ca\]
\[ \Rightarrow ab + bc + ca\]
So this is the required addition of the given expressions.
So this is the required answer.

Note: Whenever we face such types of problems the key thing that we need to take care of is that the coefficients of the like terms play a major role in deciding the output while performing alphabetical addition. This concept will help to get on the right track to reach the answer.