Question

Subtract (ab-bc-ca) from (–ab+bc+ca)?

Answer 1

Hint: To do algebraic operations on the variables, we have to keep in mind the functionality, that is how variables work. On dealing with variables we should consider that variables can also be treated as numbers only the thing is on addition and subtraction, the coefficients of variables are dealt with.

Complete step-by-step solution:
The given question is asked to subtract the terms given, here to solve this question first we need to write the given terms, after applying the mathematical operation that is subtraction, and then on simplifying we can get the final result. Here for this question the variables given are in product of two different variable, hence we have to keep in mind that addition and subtraction in variables are possible for same kind of terms only, on simplifying we get:
\[
   \Rightarrow (ab - bc - ca) - ( - ab + bc + ca) \\
   \Rightarrow (ab - bc - ca) + ab - bc - ca \\
   \Rightarrow ab - bc - ca + ab - bc - ca \\
   \Rightarrow 2(ab - bc - ca) \\
 \]
Here we got the final result after simplification.

Note: Here when algebraic operations need to be done on variables, simplification should always be done keeping in mind the sign attached with the variable. Signs are very important to deal with, otherwise the answer can be completely opposite to the correct one.