How do you factor #y^3 - 125#?
1 Answer
Dec 21, 2015
Use the difference of cubes identity to find:
#y^3-125 = (y-5)(y^2+5y+25)#
Explanation:
The difference of cubes identity can be written:
#a^3-b^3=(a-b)(a^2+ab+b^2)#
Use this with
#y^3-125#
#=y^3-5^3#
#=(y-5)(y^2+(y)(5)+5^2)#
#=(y-5)(y^2+5y+25)#
The remaining quadratic factor has a negative discriminant, showing that it has no linear factors with Real coefficients.
If we are allowed Complex coefficients then we can factor a little further:
#=(y-5)(y-5omega)(y-5omega^2)#
where