MathWithNaziaa : Addition and subtraction of algebraic expression

Addition and subtraction of algebraic expression

       

              Addition and subtraction of integers are similar to Addison and subtraction of numbers. A combination of variables, constants and operators Combine to form an algebraic expression.In case of algebraic expression we need to Sort out the like and unlike terms Together. 

Addition of algebraic expression:

When adding algebraic expressions we add only the like terms when two like terms are added and add only the coefficient of the like terms.

           There are two ways to add  algebraic expression, they are

• Horizontal method

• Column method

 Horizontal method:

              In this method all expressions are written and horizontal line then we group the like terms together.The coefficient of the like terms are added.Together using simple addition techniques and the variables which is common is retained as it is.The unlike terms are retained as it is in the result obtained.Is the addition of two or more algebraic expression.

 for example:

1) (7a +24b-2c) , (2a-5b-4c) = 7a + 24b - 2c + 2a - 5b -4c

                                             = 7a + 2a + 24b - 5b - 2c - 4c

                                             = 9a + 19b -6c

2) (-6a +4b -3c ) ,( 7b - 4c + 2a) = -6a + 4b - 3c + 7b -4c +2a

                                                   = -6a +2a + 4b +7b -3c - 4c

                                                   = -4a +11b -7c

Column method:

               In this method expressions are arranged in separate rows, the like terms are arranged one below the another in a column wise.

 For example :

1.  (7a +24b-2c) , (2a-5b-4c) 

      

             7a + 24b - 2c 

             2a - 5b    - 4c

           —---------------------

             9a +19b - 6c

           —--------------------

2. (-6a +4b -3c ) ,( 7b - 4c + 2a)

                      - 6a + 4b - 3c

                      +2a + 7b - 4c

                    —-------------------

                       - 4a + 11b -7c

                   —--------------------

Subtraction of algebraic expression

                          To subtract or more algebraic expression.It is.A best practise to write the expression to be subtracted below.The expression from which it is to be subtracted from. Like terms are.Placed below each other. while subtracting an algebraic expression from another,  we should change the sign ( from + to - or - to + ) of all the terms which are to be subtracted. 

Steps to be followed for subtraction of algebraic expressions:

• Arrange the expression in the same order

•  arrange the expression in two rows such that the like terms occur one below the other keep the subtrahend in the second row.

• Change the sign of each term in the second row “+” to “-” and vice versa 

• Add /  subtract with the new sign in the second row 

For example:

1. 4x2+ 3x - 8 from 9 - x- 3x2

     

                - 3x2 -   x+ 9

                  4x2 + 3 x - 8

                -      -         +

             —--------------------

               - 7x2 - 4 x+ 17

           —-----------------------

2. 7x2 y+ 3 xy² - 8z from  -4xy² + 7 z- 6 x²y 

                                    - 4xy² + 7z - 6x²y

                             3xy² - 8 z+ 7x²y

                            -        +       -

                      —----------------------------

                           - 7xy² + 15z- 13x²y

                     —------------------------------      

               

Practise problems.

1. Add 8a³b³+ 4ab³ - 2a²b³ and 8a²-a²b³+4ab³

2. Subtract 44x4+17x3+x-18 from  54x4- 33x3 -28x2+7x - 6

3. Simplify (10x2+14) + (9x2+3 ) -( 8x2-6)

4. Simplify (29x3- 11x+30) - (17x3-8x - 22)