Question

factor out the common monomial factor y.
$x^2y - 9xy^2 + y^3 = y \cdot (\text{(no response)} \quad x^2 - 9xy + y^2)$

step 2
can you find two numbers whose sum is $(-9)$ and product is 1?
\bigcirc yes
\bigcirc no (selected)

this indicates that the trinomial $x^2 - 9xy + y^2$ is (selected) prime.

step 3
the complete factorization is the following.
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Explanation:

Step1: Factor out monomial $y$

$x^2y - 9xy^2 + y^3 = y(x^2 - 9xy + y^2)$

Step2: Check trinomial primality

No integers sum to $-9$ and product to $1$, so $x^2 - 9xy + y^2$ is prime.

Step3: State full factorization

Retain the factored form with prime trinomial.

Answer:

$y(x^2 - 9xy + y^2)$