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

Jun 9, 2016

$\left(y - 1\right) \left({y}^{2} + 1\right)$

#### 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
$\left({y}^{3} - {y}^{2}\right) + \left(y - 1\right)$
Taking out common factor
$\implies {y}^{2} \left(y - 1\right) + \left(y - 1\right)$
Taking out the common factor $\left(y - 1\right)$ out of the two terms we obtain
$\implies \left(y - 1\right) \left({y}^{2} + 1\right)$
We have our required factors.