How do you factor #y^3-y^2+y-1 # by grouping?

1 Answer
Jun 9, 2016

Answer:

#(y-1)(y^2+1)#

Explanation:

Given expression is
#y^3-y^2+y-1#

  1. On inspection we notice that first two terms have a common factor #y^2#.
  2. if we take out #y^2# common out of these two what remains is equal to the last two terms.
  3. The last two do not have any common factor except #1#.

Let us therefore group first two and last two terms. We rewrite the expression as
#(y^3-y^2)+(y-1)#
Taking out common factor
#=> y^2(y-1)+(y-1)#
Taking out the common factor #(y-1)# out of the two terms we obtain
#=> (y-1)(y^2+1)#
We have our required factors.