multiplication by use of detached coefficient

Multiply (x - 3x² +x³) (x +2x³-x⁵ ) as far as 4^th power of x.

In using this method of detached coefficients the coefficients must be arranged in ascending power of x. 

x²            x³                  x⁴            x⁵                   ...... x⁸

1              0              2              0              1

1              -3            1                             

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

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

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

1              -3            3                                   are the coefficients of rising power of x from left to right

Note we have restricted all multiplications to x⁴.

So, the answer is x² - 3x³ + 3x⁴