Question

How do you add like terms in \[3a - 7b + 4c - 12 + 5b - 2a + 23 - 8c\] ?

Answer 1

Hint: We have an addition and subtraction of an algebraic expression. AN algebraic expression is a combination of constants, variables and operators. The addition and subtraction of algebraic expressions are quite similar to the addition and subtraction of the number, when it comes to algebraic expression we must sort the like terms and unlike terms together.

Complete step by step solution:
Given,
\[3a - 7b + 4c - 12 + 5b - 2a + 23 - 8c\]
We have a simple algebraic expression,
Now group the like terms, that is the number which contains ‘a’.
\[ \Rightarrow \left( {3a - 2a} \right) - 7b + 4c - 12 + 5b + 23 - 8c\]
Now group the number contains ‘b’
\[ \Rightarrow \left( {3a - 2a} \right) + \left( { - 7b + 5b} \right) + 4c - 12 + 23 - 8c\]
Now group the number contains ‘c’
\[ \Rightarrow \left( {3a - 2a} \right) + \left( { - 7b + 5b} \right) + \left( {4c - 8c} \right) - 12 + 23\]
Lastly we group constants that are only numbers.
\[ \Rightarrow \left( {3a - 2a} \right) + \left( { - 7b + 5b} \right) + \left( {4c - 8c} \right) + \left( {23 - 12} \right)\]
Now adding and subtracting we have,
\[ \Rightarrow \left( a \right) + \left( { - 2b} \right) + \left( { - 4c} \right) + \left( {11} \right)\]
That is we have,
\[ \Rightarrow a - 2b - 4c + 11\] . This is the required answer.
So, the correct answer is “\[ a - 2b - 4c + 11\] ”.

Note: You must be aware of the like and the unlike terms when you are adding or subtracting algebraic expressions. We can only perform the addition or subtraction on the like terms only. Like terms are the ones who have the same variables and exponents and the unlike terms are the one that have different variables. Here \[ \Rightarrow a - 2b - 4c + 11\] , ‘a’, ‘b’ and ‘c’ are different variables so we cannot simplify further.