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Home >> Polynomials >> Subtraction of Polynomials >> Subtraction of Binomials >> Subtraction of Binomials
Before you study this concept, you are advice of read:
What are Like Terms ?
What are Unlike Terms ?
How to subtract Like Terms ?
During subtraction of Binomials we are encountered with the following three situations:
Subtraction of Binomials having like terms
Subtraction of Binomials having unlike terms
Subtraction of Binomials having both like and unlike terms
Subtraction of Binomials having like terms is done in the following steps:
Step 1: Arrange the binomials in like terms
Step 2: Subtract one like terms from another like term
Example 1: Subtract 10ab + 5 from 12ab + 10
Solution: Given two binomials are:
First Binomial = 10ab + 5
Second Binomial = 12ab + 10
Now subtraction of given binomials is done as follows:
(12ab + 10) - (10ab + 5)
Open the brackets and we get:
= 12ab + 10 - 10ab - 5
Rearrange them into like terms and we get:
= 12ab - 10ab + 10 - 5
Solve Subtraction of like terms and we get:
= 2ab + 5
Hence, (12ab + 10) - (10ab + 5) = 2ab + 5
Example 2: Subtract 4yx2 + 5a from 5yx2 + 2a
Solution: Given two binomials:
First Binomial = 4yx2 + 5a
Second Binomial = 5yx2 + 2a
Now subtraction of given binomials is done as follows:
(5yx2 + 2a) - (4yx2 + 5a)
Open the brackets and we get:
= 5yx2 + 2a - 4yx2 - 5a
Rearrange them into like terms and we get:
= 5yx2 - 4yx2 + 2a - 5a
Solve subtraction of like terms and we get:
= yx2 + (-3a)
Open bracket and we get
= yx2 - 3a
Hence, (5yx2 + 2a) - (4yx2 + 5a) = yx2 - 3a
Subtraction of Binomials having unlike terms:
Here we must note that one binomial can be subtracted from another binomial only when both have like terms.
Or we can also say that:
Binomials having unlike terms cannot be subtracted from each other.
E.g. Binomial (2x + 1) cannot be subtracted from another binomial (3y + 5x2).
Subtraction of Binomials having both like and unlike terms
In such situations you will notice that binomials in the subtraction operation have like as well as unlike terms. So in such situations we do the subtraction of like terms and keep unlike terms as such.
Example 1 : subtract 24p - x from 10p + 2
Solution: Given two binomials:
First Binomial = 24p - x
Second Binomial = 10p + 2
Now subtraction of given binomials is done as follows:
(10p + 2) - (24p - x)
Open brackets and we get:
= 10p + 2 - 24p + x
Rearrange them into like terms and unlike terms & we get
= 10p - 24p + x + 2
Solve subtraction of like terms and keep unlike terms as such & we get:
= (-14p + x + 2)
Hence, (10p + 2) - (24p - x) = (-14p + x + 2)
Example 2 : Solve (5yx2 + 2ab) - (4x2 + 5ab)
Solution: Given two binomials:
First Binomial = 5yx2 + 2ab
Second Binomial = 4x2 + 5ab
Now Subtraction of given binomials is done as follows:
(5yx2 + 2ab) - (4x2 + 5ab)
Open brackets and we get:
= 5yx2 + 2ab - 4x2 - 5ab
Rearrange them into like terms and unlike terms & we get
= 5yx2 - 4x2 + 2ab - 5ab
Subtract like terms and keep unlike terms as such & we get:
= 5yx2 - 4x2 - 3ab
Hence, (5yx2 + 2ab) - (4x2 + 5ab) = 5yx2 - 4x2 - 3ab
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