Step-by-Step Guide to Adding Algebraic Expressions

algebraic expressionsDo you feel stuck while adding algebraic expressions? If your answer to this question is simply yes, don’t worry; you are not alone. Every new learner goes through this situation while solving a new mathematical problem. While mathematical operations are tricky to solve, learning the right strategies to solve mathematical operations can take your education journey to a new level. 

We at the 98th percentile have curated a step-by-step guide that will help you tackle all the challenging problems with the addition of algebraic expressions. Don’t forget to note down the tricks and tips for future reference. Without any delay, let us jump into learning together in a strategic way

What are Algebraic Expressions?

Algebraic expressions are basic mathematical expressions that include constants, variables, coefficients, and operators. For example, 2x+3y+35. Let us dig into the topic more deeply and see what these constituent elements of algebraic expressions are. 

  • Constants: Constants are simple numbers that we have been encountering since our early school days. Constants can be positive and negative.  For example, -3, 2, 13, 100, etc.

  • Variable: Variables are some symbols that define unknown values. Generally, variables are represented using small alphabet letters. For example, x, y, z, a, b, p, etc.

  • Coefficient: coefficients are the numbers that are multiplied by variables. For example, 2x, 4p, 678a, etc.

  • Operators: Operators are symbols that represent mathematical operations. For eg: + (addition), - (subtraction), × (multiplication), and ÷ (division).

  • Terms: Each part separated by operators is called a term. For example, in 2x+3y+35  terms are 2x, 3y, and 35.

Fun fact about algebraic expressions: Algebraic expressions don’t include = (equal), otherwise they will become algebraic equations

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Steps to Follow  for Adding Algebraic Expression

  • Determine the like terms:  Like terms are the terms that have the same variable. For eg:  Let

      3x+4y+23 be expression 1


     5x+32    be expression 2

     3x and 5x are like terms but   4y and 5x are not like terms. 

  • Arrange the expressions:  arrange the expressions that are to be added using brackets. 

     eg: arranging expression 1 and expression 2 

     we get

     (3x+4y+23)  +  (5x+6y-32), let this be expression 3.

  • Combine Like terms:  combine the like terms from expression 3. 

     (3x + 5x) + (4y + 6y) + 23 - 32, let this be expression 4. 

  • Perform the addition: From expression 4, 

Add the coefficients of the like terms 

eg:   for the variable x:  3 and 5 are coefficients so we get (3+5)x i.e. 8x.

And for variable y: 4 and 6 are coefficients so we get (4+6)y i.e. 10y.

      Add the constants:   for expression 4 constants are 23 and -32; adding the two constants we get        -9.

  • Final result: Assemble the expression to get the result. For the above example, the result is 8x+10y-9. 

Solved Examples of the AdditionofAlgebraic Expressions

Example 1:  Let us take algebraic expressions E1, E2, and E3 as following: 

E1: 4x+3y+3 

E2: 4y+2

E3: 2x-y-12


=( 4x+3y+3 ) + ( 4y+2 ) + ( 2x-y-12)

= (4x+2x) + (3y+4y-y) +3+2-12

=6x + 6y -7

Example 2:  Let us take algebraic expressions E1, E2, and E3 as following: 

E1: 2x+3y+9 

E2: 5x+23

E3: 2x-y-12


=( 2x+3y+9 ) + ( 5x+23 ) + ( 2x-y-12)

= (2x+5x+2x) + (3y-y) +9+23-12


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FAQs (Frequently Asked Questions)

Q1: Can variables have constants added to them?

Ans: No, only like terms may be added. Terms with variables can only be added to other terms that have the same variable(s) and exponent(s). Constants, or numbers without variables, can be added to other constants.

Q2: What happens if the variables in the algebraic expressions differ?

Ans: You can only mix like terms when adding algebraic formulas with distinct variables. In 2 𝑥 + 3 𝑦 2x+3y and 4 𝑥 + 5 𝑧 4x+5z, for instance, you can combine 2 𝑥 2x and 4 𝑥 4x to create 6 𝑥 6x, but 3 𝑦 3y and 5 𝑧 5z stay apart.

Q3: What typical errors should one avoid while combining expressions in algebra?

Ans: Typical errors include arithmetical errors, improper combination of like terms, and failure to distribute negative signs during subtraction.

Q4: In what way may the addition of algebraic expressions be verified?

Ans: By changing certain values for the variables and ensuring that the result produced by the original and simplified formulations is the same, you may validate the addition.

Q5: Why is learning how to add algebraic expressions important?

Ans: A key algebraic skill for solving equations, reducing expressions, and comprehending more complex mathematical ideas is adding algebraic expressions.

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