Adding one algebraic symbol to another algebraic symbol by placing all symbols in a row and connecting them by a plus sign is defined as the addition of algebraic symbols using row method.

In row method, algebraic symbols are written in a row but place a plus sign between every two algebraic symbols to perform summation with algebraic symbols.

The process of adding like symbols, unlike symbols and combination of both is same but sum of like symbols forms an algebraic term, sum of unlike symbols forms an algebraic expression and summation of both types of symbols also forms algebraic expressions. These three cases are possible cases of adding algebraic symbols in algebraic system.

1.

Addition of Like symbols

Consider an algebraic symbol $a$ and it is an alphabetic letter. Take the letter one more time and write them in a row by placing a plus sign between them.

$a+a$

The two letters are like. So, they can be combined as a single letter but the total letters should be written before to that letter.

$a+a=2a$

Use this procedure to add two or more like symbols using row method. You can understand it from more examples.

$b+b+b=3b$

$c+c+c+c=4c$

$d+d+d+d+d=5d$

It can be written in general form.

$x+x+x+\dots +x(nsymbols)=nx$

Addition combines all like algebraic symbols as a single algebraic term.

2.

Addition of Unlike Symbols

The symbols which are denoted by different symbols cannot be combined as an algebraic term due to the unlike property. Therefore, unlike algebraic symbols always form algebraic expressions.

$a$ and $b$ are two unlike algebraic symbols. Write two algebraic symbols in a row by placing a plus sign between them.

$a+b$

These two algebraic symbols are unlike. So, they cannot be combined as an algebraic term but except writing them as an algebraic expression. You can see many more examples here.

$a+b+c$

$a+b+c+d$

$a+b+c+d+e$

3.

Take an algebraic letter $a$ four times and also consider two unlike algebraic letters $b$ and $c$. Write all of them in a row by placing a plus sign between every symbols.

$a+a+a+a+b+c$

Combine addition of like and addition of unlike symbols methods to get the sum of addition of both types of symbols using row method. There are four like algebraic symbols and remaining are unlike letters. So, combine all like algebraic letters and then write the unlike algebraic letters as an expression.

$4a+b+c$

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