Algebric multiplication using detached coeffficient

Use of detached coefficients in multiplication

I will try to explain this using an example:

Say we want to multiply (2x³ – 4x² – 5) by (3x² + 4x – 2)

In 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.

2              -4            0              -5

3              +4           -2            

6              -12          0              -15                                 (multiplying 3 with all the above numbers)

                8              -16          0              -20                   ( 4 with all the above numbers)

                                -4            8              0              10      ( -2 with all the above numbers)

6              -4            -20          -7            -20          10  

The bold numbers are the coefficients of rising power of x from right to left

So, the answer is 

6x⁵ – 4x⁴ – 20x³ – 7x² – 20x + 10