How do you factor #27x^3-512#?
1 Answer
Dec 17, 2015
Use the difference of cubes identity to find:
#27x^3-512 = (3x-8)(9x^2+24x+64)#
Explanation:
The difference of cubes identity may be written:
#a^3-b^3=(a-b)(a^2+ab+b^2)#
Notice that
#27x^3-512#
#=(3x)^3-8^3#
#=(3x-8)((3x)^2+(3x)(8)+8^2)#
#=(3x-8)(9x^2+24x+64)#
If you allow Complex coefficients then this factors a little further:
#=(3x-8)(3x-8omega)(3x-8omega^2)#
where