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Home >> Polynomials >> Addition of Polynomials >> Addition of Binomials >> Addition of Binomials
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 Binomials we are encountered with the following three situations:
Addition of Binomials having like terms
Addition of Binomials having unlike terms
Addition of Binomials having both like and unlike terms
Addition of Binomials having like terms is done in the following steps:
Step 1: Arrange the binomials in like terms
Step 2: Add like terms
Example 1: Add 12ab + 10 and 10ab + 5
Solution: Given two binomials:
First Binomial = 12ab + 10
Second Binomial = 10ab + 5
Now addition 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
Add like terms and we get:
= 22ab + 15
Hence, (12ab + 10) + (10ab + 5) = 22ab + 15
Example 2: Add 5yx2 + 2a , 4yx2 + 5a and 7yx2 + 7a
Solution: Given three binomials:
First Binomial = 5yx2 + 2a
Second Binomial = 4yx2 + 5a
Third Binomial = 7yx2 + 7a
Now addition of given binomials is done as follows:
(5yx2 + 2a) + (4yx2 + 5a) + (7yx2 + 7a)
Open the brackets and we get:
= 5yx2 + 2a + 4yx2 + 5a + 7yx2 + 7a
Rearrange them into like terms and we get:
= 5yx2 + 4yx2 + 7yx2 + 2a + 5a+ 7a
Add like terms and we get:
= 16yx2 + 14a
Hence, (5yx2 + 2a) + (4yx2 + 5a) + (7yx2 + 7a) = 16yx2 + 14a
Addition of Binomials having unlike terms:
Here we must note that two or more binomials are added only when both have like terms.
Or we can also say that:
Binomials having unlike terms cannot be added.
E.g. Binomials 2x - 1, 3y + 5x2, 10p - 4b, 32q + 10c cannot be added because all have unlike terms.
Addition of Binomials having both like and unlike terms
In such situations you will notice that binomials 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 + 2, 24p + x
Solution: Given two binomials:
First Binomial = 10p + 2
Second Binomial = 24p + x
Now addition 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
Add like terms and keep unlike terms as such & we get:
= 34p + x + 2
Hence, (10p + 2) + (24p + x) = 34p + x + 2
Example 2 : Add 5yx2 + 2ab , 4x2 + 5ab and 7x2 + 7
Solution: Given three binomials:
First Binomial = 5yx2 + 2ab
Second Binomial = 4x2 + 5ab
Third Binomial = 7x2 + 7
Now addition of given binomials is done as follows:
(5yx2 + 2ab) + (4x2 + 5ab) + (7x2 + 7)
Open brackets and we get:
= 5yx2 + 2ab + 4x2 + 5ab + 7x2 + 7
Rearrange them into like terms and unlike terms & we get
= 5yx2 + 4x2 + 7x2 + 5ab + 2ab + 7
Add like terms and keep unlike terms as such & we get:
= 5yx2 + 11x2 + 7ab + 7
Hence, (5yx2 + 2ab) + (4x2 + 5ab) + (7x2 + 7) = 5yx2 + 11x2 + 7ab + 7
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