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Home >> Algebraic Expression >> Subtraction Expression (Algebra) >>

Subtraction Expression in Algebra

Addition Expression (Algebra) Division Expression (Algebra) Multipication Expression (Algebra) Subtraction Expression (Algebra) Terms of Algebraic Expression
Value of an Algebraic Expression Tree Diagram for Algebraic Expression Constants Variables

  • What is Subtraction Expression

    Explanation :-
    Subtraction Expression in algebra includes
    Literal Numbers
    Subtraction Operator
    constants

    For example = (x y), (a 7), (4 b)
    In the above example we have :-
    Subtraction Operator i.e. (-),
    Literal Numbers = x, y, a, b and
    Constants = 7, 4.

    Subtraction Expression in Algebra is of the following two types:-

    1). Difference of Literal Numbers :-
    It includes subtraction operator (-), and literal numbers.
    For example =(x y), (p q), (a b).
    In the above example we have:-
    Subtraction Operator i.e. (-)
    Literal Numbers = x, y, p, q, a, b
    Note :- In this type of expression, we don't have any constants.

    2). Difference of Literal Numbers and Constants.
    It includes subtraction operator (-), literal numbers and constants
    For example = (x 5), (7 q), (a b 4)
    In the above example we have :-
    Subtraction Operator i.e. (-)
    Literal Numbers = x, q, a, b and
    Constants = 5, 7, 4.








    Subtraction of Algebraic Expressions

    Before you further read, you are advice to read:

    What are Terms of Algebraic Expression ?
    What are Like Terms ?
    What are Unlike Terms ?
    Subtraction of Like Terms ?

    During subtraction of algebraic expression we are encountered with the following three situations:
    Subtraction of algebraic expression having like terms
    Subtraction of algebraic expression having unlike terms
    Subtraction of algebraic expression having both like and unlike terms

    Let's study these in details which is as follows -

    1) Subtraction of algebraic expression having like terms involves following steps:

    Step 1: Rearrange the terms of given algebraic expression into like-terms
    Step 2: Subtract one like term(s) from another like term(s)

    Example : Solve (2a + 3b 4x + 5y 6) - (-7a - 8b + 9x + 10y 11)
    Solution: Given two algebraic expression

    First Algebraic expression = 2a + 3b 4x + 5y 6
    Second Algebraic expression = (-7a - 8b + 9x + 10y 11)

    Now subtraction of given algebraic expression is done as follows:
    (2a + 3b 4x + 5y 6) - (-7a - 8b + 9x + 10y 11)

    Open brackets and we get:
    = 2a + 3b 4x + 5y 6 + 7a + 8b - 9x - 10y + 11

    Rearrange the terms of given algebraic expression into like-terms and we get:
    = 2a + 7a + 3b + 8b 4x 9x - 10y + 5y 6 + 11

    Add like terms and we get:
    = 9a + 11b - 13x - 5y + 5

    Hence, (2a + 3b 4x + 5y 6) - (-7a - 8b + 9x + 10y 11) = 9a + 11b - 13x - 5y + 5


    2) Subtraction of algebraic expression having like terms

    Here we must note that subtraction of algebraic expression is possible only when both have like terms.
    Or we can also say that:
    Algebraic expressions having unlike terms cannot be subtracted from each other.
    E.g. 3y + 5t 9a + 5x2 cannot be subtracted from 10p + t3 - 4b 8r because both have unlike terms.


    3) Subtraction of algebraic expression having both like and unlike terms

    In such situations you will notice that algebraic expressions in subtraction operation have like as well as unlike terms. So in such situations we subtract one like term(s) from another like term(s) and keep unlike terms as such.

    Example : Solve ( 2x3 + 3x2 + 10y 2) (x3 - 4x2 + 9x c)
    Solution: Given two algebraic expression

    First Algebraic expression = 2x3 + 3x2 + 10y - 2
    Second Algebraic expression = x3 - 4x2 + 9x - c

    Now subtraction of given algebraic expression is done as follows:
    ( 2x3 + 3x2 + 10y 2) - (x3 - 4x2 + 9x c)

    Open brackets and we get:
    = 2x3 + 3x2 + 10y 2 - x3 + 4x2 - 9x + c

    Rearrange them into like terms and unlike terms & we get
    = 2x3 - x3 + 3x2 + 4x2 + 10y - 9x + c 2

    Add like terms and keep unlike terms as such & we get:
    = 3x3 + 7x2 + 10y + 9x c - 2

    Hence, ( 2x3 + 3x2 + 10y 2) - (x3 - 4x2 + 9x c) = ( 3x3 + 7x2 + 10y + 9x c - 2)



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