SOLUTION: 1. Factor x⁸ - 256 2. Multiply out, collect terms and arrange in descending order (2x - 3)(x + 1)(3x - 2)

1. Factor x8 - 256

x8 - 256

Write this as

(x4)2 - 162

This is the difference of two squares and factors as the 
product of the difference and sum of the square roots of the 
squares:

(x4 - 16)(x4 + 16)

Now write the first parentheses as [(x2)2 - 42].

[(x2)2 - 42](x4 + 16)

The bracketed expression is also the difference of two squares
and factors as the product of the difference and sum of the 
square roots of the squares. Please note that the second factor 
(the one in parentheses) is the SUM or two squares, which is NOT
factorable.

(x2 - 4)(x2 + 4)(x4 + 16)

Now write the first parenthetical factor as

(x2 - 22)(x2 + 4)(x4 + 16)

The first parenthetical expression is also the difference of two 
squares and factors as the product of the difference and sum of 
the square roots of the squares. Please note as before that the 
second and third parenthetical factors are SUM or two squares, 
which are not factorable.

(x - 2)(x + 2)(x2 + 4)(x4 + 16)

That's now completely factored.

2. Multiply out, collect terms and arrange in descending order
   (2x - 3)(x + 1)(3x - 2)

   (2x - 3)(x + 1)(3x - 2)

Multiply the first two using "FOIL":

   (2x2 + 2x - 3x - 3)(3x - 2) 

Combine " + 2x - 3x " as " - x "

   (2x2 - x - 3)(3x - 2)

Rewrite the first factor as 

   [(2x2 - x) - 3](3x - 2)

and use "FOIL" again where the entire red factor is to be considered
as the "FIRST" on the left

   (2x2 - x)(3x) - 2(2x2 - x) - 9x + 6

Completing the multiplication:

   6x3 - 3x2 - 4x2 + 2x - 9x + 6

Combining like terms:

   6x3 - 7x2 - 7x + 6 

Edwin
AnlytcPhil@aol.com