Vertical Method of Multiplication of Algebraic Expression –

Steps.1) We first multiply each term of first expression by each term of second expression, then write the subtrahend (that is, the expression to be added) below the minuend (that is, the expression from which to subtract) in such a way that the like terms are in the same column.

Steps.2) Change the sign of each term of the subtrahend.

Steps.3) Then we have to add the expression.

There are some examples are given below for your better understanding

Example.1) Find the product of  (3x+5y) by (2a – 7b)

Ans.) For convenience, we arrange the terms of the polynomial in descending power of x

      3x + 5y

      2a – 7b


      6ax + 10ay                 [ multiplying 3x + 5y by 2a ]

  - 21bx – 35by                  [ multiplying 3x + 5y by (-7b)]


6ax + 10ay - 21bx – 35by        [ adding in columns ]        (Ans.)


Example.2) Find the product of  (5x+3y – 4z ) by (3xy – 7yz + 4zx)

Ans.)   5x + 3y – 4z

         3xy – 7yz + 4zx


        15x²y + 9xy²- 12xyz     [multiplying 5x + 3y – 4z by 3xy]

                       - 35xyz – 21y²z + 28yz² [multiplying 5x+3y–4z by                                                                                                                    + 12xyz                 20x²z –16xz² [multiplying 

                                                               5x+3y–4z by 4zx]


       15x²y + 9xy² – 35xyz – 21y²z + 28yz² + 20x²z – 16xz²         

                                                                 [adding in columns]