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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