Question

factor the trinomial completely. (if the expression is not factorable using integers, enter prime.)
$x^{2}y - 4xy^{2} + y^{3}$

Explanation:

Step1: Factor out GCF

Identify and factor out the greatest common factor $y$ from each term.
$x^2y - 4xy^2 + y^3 = y(x^2 - 4xy + y^2)$

Step2: Check for integer factorization

Examine the quadratic $x^2 - 4xy + y^2$; no integer pairs multiply to $y^2$ and add to $-4y$.
The quadratic cannot be factored further with integers.

Answer:

$y(x^2 - 4xy + y^2)$