Answer
not factorable with integer coefficients
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Then, express the factored form as $(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
In the given expression, $
x^2y^2+12xy+18
,$ the value of $c$ is $
18
$ and the value of $b$ is $
12
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{1,18\}, \{2,9\}, \{3,6\},
\{-1,-18\}, \{-2,-9\}, \{-3,-6\}
.\end{array}
Among these pairs, none gives a sum of $b.$ Hence, the given expression is $\text{
not factorable with integer coefficients
.}$