Study MaterialsAddition of Algebraic Expressions | Adding Algebraic Expressions, Solved Examples

Addition of Algebraic Expressions | Adding Algebraic Expressions, Solved Examples

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems. We have explained clear ways to find the Addition of Algebraic Expressions. We even provided different examples for different methods to solve the addition of algebraic expressions. Therefore, check practice questions, answers, and explanations for every problem and get the best knowledge to solve algebraic expressions.

Methods to Solve an Addition of Algebraic Expressions

Students can perform the addition of algebraic expressions using two methods. Use the best and easy method for you and find the final expression. The two methods to find the addition of algebraic expressions are given below.
1. Horizontal Method
2. Column Method

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    How to find the addition of algebraic expressions using the Horizontal Method?

    The Horizontal Method is the simplest way to find the addition of algebraic expressions. Just by following the below step by step procedure, students can estimate the addition of algebraic expressions.

    • Firstly, note down the given expressions.
    • Place the given expressions in a row and separate them with the addition symbol in between them.
    • Re-arrange the given terms by grouping or placing like terms together.
    • Simplify the coefficients of like terms.
    • Finally, write the resultant expression in standard form.

    How to find the addition of algebraic expressions using the Column Method?

    The Column method is also called a Vertical Method. The Addition of Algebraic Expressions can be estimated using the vertical method by writing expressions in separate rows. Before you write separate rows, you need to arrange the expressions with like terms in the correct order. Have a look at the below procedure to exactly know what is the process to find the addition of algebraic expressions using the Column Method.

    • Write the given expressions.
    • Place one expression below the other expression with the like terms come in the same column.
    • Next, add the like terms column-wise with their coefficients.
    • Finally, fins the resultant expression in the standard form.

    Addition of Algebraic Expressions Solved Examples

    1. Add 5a + 7b – 6c, b + 2c – 3a and 2a – 5b – 3c

    Solution:Given expressions are 5a + 7b – 6c, b + 2c – 3a and 2a – 5b – 3c.

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    5a + 7b – 6c + b + 2c – 3a + 2a – 5b – 3c.
    Arrange the like terms together.
    5a – 3a + 2a + 7b + b – 5b – 6c + 2c – 3c.
    Now, find the sum of the numerical coefficients of all terms.
    4a + 3b – 7c.

    The required expression is 4a + 3b – 7c.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    5a + 7b – 6c, – 3a + b + 2c, 2a – 5b – 3c
    Note down the like terms below each other and add them in column-wise.
    + 5a + 7b – 6c
    – 3a + b + 2c
    + 2a – 5b – 3c
    —————————-
    4a + 3b – 7c

    The required expression is 4a + 3b – 7c.

    2. Add 7x² + 8y – 9, 3y + 2 – 3x² and 3 – y + 3x².

    Solution:
    Given expressions are 7x² + 8y – 9, 3y + 2 – 3x² and 3 – y + 3x².

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    7x² + 8y – 9 + 3y + 2 – 3x² + 3 – y + 3x².
    Arrange the like terms together.
    7x² – 3x² + 3x² + 8y + 3y – y – 9 + 2 + 3.
    Now, find the sum of the numerical coefficients of all terms.
    7x² + 10y – 4.

    The required expression is 7x² + 10y – 4.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    7x² + 8y – 9, – 3x² + 3y + 2 and + 3x² – y + 3
    Note down the like terms below each other and add them in column-wise.
    + 7x² + 8y – 9
    – 3x² + 3y + 2
    + 3x² – y + 3
    —————————-
    7x² + 10y – 4

    The required expression is 7x² + 10y – 4.

    3. Add 4x² – 2xy + 4y², 3xy – 5y² + 9x² and 2y² + xy – 7x².

    Solution:
    Given expressions are 4x² – 2xy + 4y², 3xy – 5y² + 9x² and 2y² + xy – 7x².

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    4x² – 2xy + 4y² + 3xy – 5y² + 9x² + 2y² + xy – 7x².
    Arrange the like terms together.
    4x² + 9x² – 7x² – 2xy + 3xy + xy + 4y² – 5y² + 2y².
    Now, find the sum of the numerical coefficients of all terms.
    6x² + 2xy + y².

    The required expression is 6x² + 2xy + y².

    4. Add 10a² + 3b² – c², 2b² + 6c² – 7a² and 3a² – 8b² – 6c².

    Solution:
    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    10a² + 3b² – c², 2b² + 6c² – 7a² and 3a² – 8b² – 6c².
    Note down the like terms below each other and add them in column-wise.
    + 10a² + 3b² – c²
    – 7a² + 2b² + 6c²
    + 3a² – 8b² – 6c²
    —————————-
    6a² – 3b² – c²

    The required expression is 6a² – 3b² – c².

    5. Add the 4x + 8y and 2x + 3y.
    Solution:
    Given expressions are 4x + 8y and 2x + 3y.

    Horizontal Method:
    There are two variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    4x + 8y + 2x + 3y
    Arrange the like terms together.
    4x + 2x + 8y + 3y
    Now, find the sum of the numerical coefficients of all terms.
    6x + 11y

    The required expression is 6x + 11y.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    4x + 8y and 2x + 3y
    Note down the like terms below each other and add them in column-wise.
    4x + 8y
    2x + 3y
    —————————-
    6x + 11y

    The required expression is 6x + 11y.

    6. Add 3x + 9y + 5 and 4x + 3y + 2

    Solution:
    Given expressions are 3x + 9y + 5 and 4x + 3y + 2.

    Horizontal Method:
    There are two variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    3x + 9y + 5 + 4x + 3y + 2
    Arrange the like terms together.
    3x + 4x + 9y + 3y + 5 + 2
    Now, find the sum of the numerical coefficients of all terms.
    7x + 12y + 7

    The required expression is 7x + 12y + 7.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    3x + 9y + 5 and 4x + 3y + 2
    Note down the like terms below each other and add them in column-wise.
    3x + 9y + 5
    4x + 3y + 2
    —————————-
    7x + 12y + 7

    The required expression is 7x + 12y + 7.

    7. Add 12x + 4y + 21z and 32x – 2y – 16z

    Solution:
    Given expressions are 12x + 4y + 21z and 32x – 2y – 16z.

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    12x + 4y + 21z + 32x – 2y – 16z
    Arrange the like terms together.
    12x + 32x + 4y – 2y + 21z – 16z
    Now, find the sum of the numerical coefficients of all terms.
    44x + 2y -5z

    The required expression is 44x + 2y -5z.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    12x + 4y + 21z and 32x – 2y – 16z
    Note down the like terms below each other and add them in column-wise.
    12x + 4y + 21z
    32x – 2y – 16z
    —————————-
    44x + 2y -5z

    The required expression is 44x + 2y -5z.

    8. Add 6x³ – 4y³ and 9x³ – 5y³
    Solution:
    Given expressions are 6x³ – 4y³ and 9x³ – 5y³.

    Horizontal Method:
    There are two variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    6x³ – 4y³ + 9x³ – 5y³
    Arrange the like terms together.
    6x³ + 9x³ – 4y³ – 5y³
    Now, find the sum of the numerical coefficients of all terms.
    15x³ – 9y³

    The required expression is 15x³ – 9y³.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    6x³ – 4y³ and 9x³ – 5y³.
    Note down the like terms below each other and add them in column-wise.
    9x³ – 5y³
    6x³ – 4y³
    —————————-
    15x³ – 9y³

    The required expression is 15x³ – 9y³.

    9. Add 3a² + 5b² + 7c² – 9abc and 2a² – 4b² + 6c² + 8abc
    Solution:
    Given expressions are 3a² + 5b² + 7c² – 9abc and 2a² – 4b² + 6c² + 8abc.

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    3a² + 5b² + 7c² – 9abc + 2a² – 4b² + 6c² + 8abc
    Arrange the like terms together.
    3a² + 2a² + 5b² – 4b² + 7c² + 6c² – 9abc + 8abc
    Now, find the sum of the numerical coefficients of all terms.
    5a² + b² + 13c² – abc

    The required expression is 5a² + b² + 13c² – abc.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    3a² + 5b² + 7c² – 9abc and 2a² – 4b² + 6c² + 8abc
    Note down the like terms below each other and add them in column-wise.
    3a² + 5b² + 7c² – 9abc
    2a² – 4b² + 6c² + 8abc
    —————————-
    5a² + b² + 13c² – abc

    The required expression is 5a² + b² + 13c² – abc.

    10. Add 2xy² + 6x²y – 9x²y – 4xy² + 5 and 3x²y + 2xy²

    Solution:
    Given expressions are 2xy² + 6x²y – 9x²y – 4xy² + 5 and 3x²y + 2xy².

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    2xy² + 6x²y – 9x²y – 4xy² + 5 + 3x²y + 2xy²
    Arrange the like terms together.
    2xy² + 2xy² + 6x²y + 3x²y – 9x²y – 4xy² + 5
    Now, find the sum of the numerical coefficients of all terms.
    4xy² + 9x²y – 9x²y – 4xy² + 5

    The required expression is 4xy² + 9x²y – 9x²y – 4xy² + 5.

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    2xy² + 6x²y – 9x²y – 4xy² + 5 and 3x²y + 2xy²
    Note down the like terms below each other and add them in column-wise.
    2xy² + 6x²y – 9x²y – 4xy² + 5
    2xy² + 3x²y +0 + 0 + 0
    —————————-
    4xy² + 9x²y – 9x²y – 4xy² + 5

    The required expression is 4xy² + 9x²y – 9x²y – 4xy² + 5.

    11. Add 2x² + 3y – 4z², 5y + 3x², 4x² + 9z² – 8y and 3y – 3x².

    Solution:
    Given expressions are 2x² + 3y – 4z², 5y + 3x², 4x² + 9z² – 8y and 3y – 3x².

    Horizontal Method:
    There are three variables available.
    Note down the like terms and then find the sum of the numerical coefficients of all terms.
    2x² + 3y – 4z² + 5y + 3x² + 4x² + 9z² – 8y + 3y – 3x²
    Arrange the like terms together.
    2x² + 3x² + 4x² – 3x² + 3y + 5y – 8y + 3y – 4z² + 9z²
    Now, find the sum of the numerical coefficients of all terms.
    6x² + 3y + 5z²

    The required expression is 6x² + 3y + 5z².

    Column Method:
    Arrange the given expressions in the same order and write them in rows. Note down the like terms below each other and add them in column-wise.
    Rearrange the given expressions.
    2x² + 3y – 4z², 3x² + 5y, 4x² – 8y + 9z² and – 3x² + 3y
    Note down the like terms below each other and add them in column-wise.
    2x² + 3y – 4z²
    3x² + 5y + 0
    4x² – 8y + 9z²
    – 3x² + 3y + 0
    —————————-
    6x² + 3y + 5z²

    The required expression is 6x² + 3y + 5z².

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