Sunday, July 21, 2013

Application of detached coefficient in multiplication

Application  of detached coefficient  in multiplication


Example: Expand (2 – x + 3x3 – x4) by (1 – 2x2 + x3 + 2x5) up to the third power of X.



Answer:

We will omit all powers of x > 3 in the multiplication. Arranging in ascending order of power of x for multiplication by the method of detached coefficient;



For multiplying (2 – x + 3x3 – x4) by (1 – 2x2 + x3 + 2x5)

For using this method the coefficients must be arranged in ascending or the descending order of power of x. 0 as coefficient must be used for missing powers of x.

x0            x1            x2            x3                  x4            x5    ..............................    x   
    
2              -1            0              3              ..             .. 

1              0              -2            1              ..             ..

2              -1            0              3              ..             ..  (multiplying 1with all the above numbers)

                0             0              0              ..            ..  (multiplying 0 with all the above numbers)

                              -4             2              ..             ..   (multiplying -2 with all the above numbers)

                                              2              ..                 (multiplying 1 with all the above numbers)

2              -1            -4            7              are the coefficients of rising power of x from left to right

Note we have restricted all multiplications to x3. This will save tremendous amount of time and effort.
So, the answer is
2 –x – 4x2 + 7x3

No comments:

Post a Comment