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Home >> Polynomials >> Subtraction of Polynomials >> Subtraction of Trinomials >> Subtraction of Trinomials
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 Trinomials we are encountered with the following three situations:
Subtraction of Trinomials having like terms
Subtraction of Trinomials having unlike terms
Subtraction of Trinomials having both like and unlike terms
Subtraction of Trinomials having like terms is done in the following steps:
Step 1: Arrange the Trinomials in like terms
Step 2: Subtract one like terms from another like term
Example 1: Subtract 10ab - 6m - 5 from 12ab - 5m + 10
Solution: Given two Trinomials are:
First Trinomial = 10ab - 6m - 5
Second Trinomial = 12ab - 5m + 10
Now subtraction of given trinomials is done as follows:
(12ab - 5m + 10) - (10ab - 6m - 5)
Open the brackets and we get:
= 12ab - 5m + 10 - 10ab + 6m + 5
Rearrange them into like terms and we get:
= 12ab - 10ab - 5m + 6m + 10 + 5
Solve Subtraction of like terms and we get:
= 2ab + m + 15
Hence, (12ab - 5m + 10) - (10ab - 6m - 5) = 2ab + m + 15
Example 2: Subtract 4yx2 + 5a + 7c from 5yx2 + 2a + 10c
Solution: Given two binomials:
First Binomial = 4yx2 + 5a + 7c
Second Binomial = 5yx2 + 2a + 10c
Now subtraction of given binomials is done as follows:
(5yx2 + 2a + 10c) - (4yx2 + 5a + 7c)
Open the brackets and we get:
= 5yx2 + 2a + 10c - 4yx2 - 5a - 7c
Rearrange them into like terms and we get:
= 5yx2 - 4yx2 + 2a - 5a + 10c - 7c
Solve subtraction like terms and we get:
= yx2 - 3a + 3c
Hence, (5yx2 + 2a + 10c) - (4yx2 + 5a + 7c) = yx2 - 3a + 3c
Subtraction of Trinomials having unlike terms:
Here we must note that one trinomial can be subtracted from another trinomial only when both have like terms.
Or we can also say that:
Trinomials having unlike terms cannot be subtracted from each other.
E.g. Trinomial (2z + 2x + 1) cannot be subtracted from another binomial (5x2 + 3m +q)
Subtraction of Trinomials having both like and unlike terms
In such situations you will notice that trinomials 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 + 9 from 10p + y - 2
Solution: Given two binomials:
First Trinomial =24p - x + 9
Second Trinomial = 10p + y - 2
Now subtraction of given trinomials is done as follows:
(10p + y - 2) - (24p - x + 9)
Open brackets and we get:
= 10p + y - 2 - 24p + x - 9
Rearrange them into like terms and unlike terms & we get
= 10p - 24p + y + x - 2 - 9
Solve subtraction of like terms and keep unlike terms as such & we get:
= (-14p + y + x - 11)
Hence, (10p + y - 2) - (24p - x + 9) = (-14p + y + x - 11)
Example 2 : Solve (5yx2 + 2ab - 10) - (4x2 + 5ab - 11)
Solution: Given two binomials:
First Binomial = 5yx2 + 2ab - 10
Second Binomial = 4x2 + 5ab - 11
Now Subtraction of given binomials is done as follows:
(5yx2 + 2ab - 10) - (4x2 + 5ab - 11)
Open brackets and we get:
= 5yx2 + 2ab - 10 - 4x2 - 5ab + 11
Rearrange them into like terms and unlike terms & we get
= 5yx2 - 4x2 + 2ab - 5ab - 10 + 11
Subtract like terms and keep unlike terms as such & we get:
= 5yx2 - 4x2 - 3ab + 1
Hence, (5yx2 + 2ab - 10) - (4x2 + 5ab - 11) = 5yx2 - 4x2 - 3ab + 1
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