Have you ever come across mathematical expressions with both letters and numbers? You may have wondered how we can apply addition operations to this mixture of numbers and letters. Well, these are nothing but algebraic expressions where the letters represent variables and numbers are constants. Let us dive and learn how algebraic expressions are added.

For a better understanding of the rules to follow let us first understand like terms and unlike terms:

Terms are the terms that have the same variable part but the coefficients can be different.

• Coefficients of like terms are added together:  Only those terms with the same variable can be added.

For example,

we can add 4xy and -6xy because the variable part here is the same i.e. xy.

To add these two terms: 4xy + (-6xy)

(4-6)xy

= -2xy

On the other hand, we can not add 4xy and 4y because the variable part of the two terms is not the same.

• Constants are added separately: If two expressions are added and both have constant terms then we add the constant terms.

For example, if E1 and E2 are two expressions such that

E1= 2x+3y+8

E2= 2y-10

E1+E2= (2x+3y+8) + (2y-10)

= 2x + 5y + (8-10)

=2x + 5y -2

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Different Ways of Algebraic Expression Addition:

The addition of algebraic expressions can be performed using two different approaches:

Horizontal Method of Addition:     In this approach, each expression is arranged using parenthesis and separated by an addition sign (+). The calculation is done step by step following the rules. ]

Let us understand this by one example:

E1: 2x+3y-10

E2: 2y+7-3x

E3: 5x+5y+5

Now  E1+E2+E3

= (2x+3y-10) + ( 2y+7-3x) + ( 5x+5y+5)

= (2x-3x+5x) + (3y+2y+5y) + (-10+7+5)

=(2-3+5)x + (3+2+5)y + (-10+12)

= 4x + 10y + 2

In this approach, we first arrange all the expressions in a similar order of variable

Then we arrange all the expressions in different rows maintaining the like terms in the same column.

This can be visualized like this:

E1: 3x-3y-3

E2: 5+6Y-3X

E3: 5X+7

E1: 3x-3y-3

E2: -3X+6y+5

E3: 5X+ 0.y+7

E1: 3x -3y -3

E2: -3X +6y +5

E3: 5X + 0y +7

(+) 5x +3y +9

More Questions to Practice Algebraic Expression Addition:

• Simplify:    2x+3y+3xy-3x-89-4x³+7yx³

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Q1: Can you add, unlike terms in algebraic expressions?

Ans: No, you can’t add, unlike terms in algebraic expressions.

Q2: How to add like terms in algebraic expressions?

Ans: Find out the like terms and add the coefficients of the like terms to get a sum of all the like terms.

Q3: What are like and unlike terms?

Ans: Like terms have the same variable part while unlike terms have different variable parts.

Q4: How can the result of the addition of algebraic expressions be simplified?

Ans: To simplify algebraic addition results, solve any parenthesis and combine the like part if any.

Q5: Can you add algebraic expressions with exponents?

Ans: No, variables with exponents are different from variables without exponents. For example, x³ is a different variable and x is a different variable.

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