How do you factor completely #y^3 - 27#?

1 Answer
Nov 22, 2015

Answer:

#y^3-27 =(y-3)(y^2+3y+9)#

Explanation:

One of the standard factor formulas is
#color(white)("XXX")#(x^3-a^3) = (x-a)(x^2+ax+a^2)#

In this case, substituting #y# for #x# and #27 = 3^3# for #a^3#
we get the answer above.

Note that in general we need to check the second factor #(y+3y+9)# for possible additional factors.
In this case the discriminant is #< 0# which tells us no additional (Real) factors are available.