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Home >> Polynomials >> Addition of Polynomials >> Addition of Trinomials >> Addition of Trinomials
Before you study this concept, you are advice of read:
What are Like Terms ?
What are Unlike Terms ?
How to add Like Terms ?
During addition of trinomials we are encountered with the following three situations:
Addition of Trinomials having like terms
Addition of Trinomials having unlike terms
Addition of Trinomials having both like and unlike terms
Addition of Trinomials having like terms is done in the following steps:
Step 1: Arrange the trinomials in like terms
Step 2: Add like terms
Example 1: Add 12ab - 5x + 10 and 10ab + 3x - 5
Solution: Given two trinomials:
First Trinomial = 12ab - 5x + 10
Second Trinomial = 10ab + 3x - 5
Now addition of given trinomials is done as follows:
(12ab - 5x + 10) + (10ab + 3x - 5)
Open the brackets and we get:
= 12ab - 5x + 10 + 10ab + 3x - 5
Rearrange them into like terms and we get:
= 12ab + 10ab - 5x + 3x + 10 - 5
Solve the above expression and we get:
= 22ab - 2x + 5
Hence, (12ab - 5x + 10) + (10ab + 3x - 5) = 22ab - 2x + 5
Example 2: Add 5yx2 + 2a - 7b, 4yx2 - 5a - 8b and 7yx2 + 8a - 9b
Solution: Given three trinomials:
First trinomial = 5yx2 + 2a - 7b
Second trinomial = 4yx2 - 5a - 8b
Third trinomial = 7yx2 + 8a - 9b
Now addition of given trinomials is done as follows:
(5yx2 + 2a - 7b) + (4yx2 - 5a - 8b) + (7yx2 + 8a - 9b)
Open the brackets and we get:
= 5yx2 + 2a - 7b + 4yx2 - 5a - 8b + 7yx2 + 8a - 9b
Rearrange them into like terms and we get:
= 5yx2 + 4yx2 + 7yx2 + 2a + 8a - 5a - 7b - 8b - 9b
Solve above expression and we get:
= 16yx2 + 5a - 24b
Hence, (5yx2 + 2a - 7b) + (4yx2 - 5a - 8b) + (7yx2 + 8a - 9b) = 16yx2 + 5a - 24b
Addition of Trinomials having unlike terms:
Here we must note that two or more trinomials are added only when both have like terms.
Or we can also say that:
Trinomials having unlike terms cannot be added.
E.g. Trinomials 2x - 1 + 3z, 3y + 5t + 5x2, 10p - 4b - 8r, 32q - 6m + 10c cannot be added because all have unlike terms.
Addition of Trinomials having both like and unlike terms
In such situations you will notice that trinomials which are to be added have like as well as unlike terms. So in such situations we add like terms and keep unlike terms as such.
Example 1 : Add 10p - 2x + 2 , 24p + x - 2m
Solution: Given two trinomials:
First Trinomial = 10p - 2x + 2
Second Trinomial = 24p + x - 2m
Now addition of given trinomials is done as follows:
(10p - 2x + 2) + (24p + x - 2m)
Open brackets and we get:
= 10p - 2x + 2 + 24p + x - 2m
Rearrange them into like terms and unlike terms & we get
= 10p + 24p - 2x + x - 2m + 2
Add like terms and keep unlike terms as such & we get:
= 34p - x - 2m + 2
Hence, (10p - 2x + 2) + (24p + x - 2m) = 34p - x - 2m + 2
Example 2 : Add 5yx2 + 2ab - 4m, 4x2 + 5ab + 2m and 7x2 + 5m - 7
Solution: Given three trinomials:
First Trinomial = 5yx2 + 2ab - 4m
Second Trinomial = 4x2 + 5ab + 2m
Third Trinomial = 7x2 + 5m - 7
Now addition of given trinomials is done as follows:
(5yx2 + 2ab - 4m) + (4x2 + 5ab + 2m) + (7x2 + 5m - 7)
Open brackets and we get:
= 5yx2 + 2ab - 4m + 4x2 + 5ab + 2m + 7x2 + 5m - 7
Rearrange them into like terms and unlike terms & we get
= 5yx2 + 4x2 + 7x2 + 2ab + 5ab - 4m + 2m + 5m - 7
Add like terms and keep unlike terms as such & we get:
= 5yx2 + 11x2 + 7ab + 3m - 7
Hence, (5yx2 + 2ab - 4m) + (4x2 + 5ab + 2m) + (7x2 + 5m - 7) = 5yx2 + 11x2 + 7ab + 3m - 7
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