Addition of unlike terms are discussed here.
The sum of two or more like terms is a single like term; but the two unlike terms cannot be added together to get a single term.
Addition of two positive unlike terms:
Suppose, to find the sum of two unlike terms x and y, we need to connect both the terms by using an addition symbol and express the result in the form of x + y.
Therefore, the sum of two unlike terms x and y = x + y.
Addition of positive and negative unlike terms:
Suppose, to find the sum of two unlike terms x and -y, we need to connect both the terms by using an addition symbol [x + (-y)] and express the result in the form of x - y.
Therefore, the sum of two unlike terms x and -y = x + (-y) = x - y.
Addition of negative and positive unlike terms:
Suppose, to find the sum of two unlike terms -x and y, we need to connect both the terms by using an addition symbol [(-x) + y] and express the result in the form of -x + y.
Therefore, the sum of two unlike terms -x and y = (-x) + y = -x + y.
Addition of negative and negative unlike terms:
Suppose, to find the sum of two unlike terms -x and -y, we need to connect both the terms by using an addition symbol [(-x) + (-y)] and express the result in the form of -x - y.
Therefore, the sum of two unlike terms -x and -y = (-x) + (-y) = -x - y.
For example:
1. The unlike terms 2ab and 4bc cannot be added together to form a single term.
All that which can be done is to connect them by the sign of addition and leave the result in the form 2ab + 4bc.
2. 5x + 3y + 2x + 3x.
= 5x + 2x + 3x + 3y.
= 10x + 3y, [Here 3y is an unlike term]
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