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Addition of Algebraic Expressions

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notes

Addition of Algebraic Expressions:

1. Addition of like terms:

  • If we have to add like terms then we can simply add their numerical coefficients.

  • The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.

  • Example: 6x + 5x = (6 + 5)x = 11x.

2. Addition of unlike terms:

  • If we have to add the unlike terms then we just have to put an addition sign between the terms.

  • Unlike terms cannot be added the way like terms are added means unlike term left as they are.

  • Example: 3xy + 7.

Addition of General Algebraic Expression:

⇒ Horizontal Steps:

  1. To add the general algebraic expressions, we have to arrange them so that the like terms come together, then simplify the terms, and the unlike terms will remain the same in the resultant expression.
  2. Add them as we add other numbers.

  3. If any term of the same variable is not there in another expression then write is as it is in the solution.

  4. Add: 3x + 11 + 8z and 7x – 5.

    The sum = 3x + 11 + 8z + 7x – 5

    Rearranging terms = (3x + 7x) + (11 – 5) + 8z = 10x + 6 + 8z

Vertical Steps:

  1. We write each expression to be added in a separate row. While doing so we write like terms one below the other.

  2. Add them as we add other numbers.

  3. If any term of the same variable is not there in another expression then write is as it is in the solution.

  4. Add: 3x + 11 + 8z and 7x – 5.
 

3x

11

8z

+

7x

-

5

   
 

10

8z

Example

Add: 7x2 - 4x + 5 and 9x – 10.
  7x2 - 4x + 5
+     9x - 10
  7x2 + 5x - 5

Example

Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xz + 5x – 2xy.
  7xy + 5yz - 3zx        
+     4yz + 9zx     - 4y
+ -2xy     - 3zx + 5x    
  5xy + 9yz + 3zx + 5x - 4y
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