Question

Add the following algebraic expression using both horizontal and vertical methods. Did you get the same answer with both methods?
$2x + 9y - 7z;3x + 3y + z;2x - 4y - z$

Answer 1

Hint: An algebraic expression is a combination of constants, variables, and operators.
In the addition of algebraic expressions, we need to collect the like terms and then add them. The sum of the several like terms would be the like term whose coefficient is the total of the coefficients of the like terms. There are two ways for solving the algebra addition:
Horizontal Method: In this method, we have to write all expressions in a horizontal line and then arrange the terms to collect all the groups of like terms and then are added.
Vertical Method: In this method, we need to write each expression in a separate row in a way that there like terms are arranged one below the other in the column. Then we have to add the terms column-wise.

Complete step-by-step answer:
On adding all the algebraic expressions: 2x+9y-7z; 3x+3y+z; 2x-4y-z
According to the Horizontal Method:
$ = \left( {2x + 9y - 7z} \right) + \left( {3x + 3y + z} \right) + \left( {2x - 4y - z} \right)$
Removing the terms from the brackets gives
$ = 2x + 9y - 7z + 3x + 3y + z + 2x - 4y - z$
Arranging the like terms together, then adding them gives you
$\begin{gathered}
   = 2x + 3x + 2x + 9y + 3y - 4y - 7z + z - z \\
   = 7x + 8y - 7z \ldots \left( 1 \right) \\
\end{gathered} $.
According to the Vertical Method:
First, write the terms of these expressions in the same order in the form of rows in a way that the like terms are below each other and then add them column-wise.
$\begin{gathered}
  2x + 9y - 7z \\
  3x + 3y + z \\
  2x - 4y - z \\
\end{gathered} $
$7x + 8y - 7z$ $ \ldots \left( 2 \right)$

Therefore, we got the same answers by both the methods.

Note: The addition and subtraction of algebraic expressions are quite similar to the addition and subtraction of the numbers. Students must be aware of the like and the unlike terms when we are adding or subtracting algebraic expressions. We can only perform the addition and subtraction on the like terms.