The determinant $\left|\begin{array}{l}{b}^2-abb-cbc-ac\\ ab-a^{2}a-b{b}^2-ab\\ bc-acc-aab-a^2\end{array}\right|$equal to

we have,

$\left|\begin{array}{l}{b}^2-abb-cbc-ac\\ ab-a^{2}a-b{b}^2-ab\\ bc-acc-aab-a^2\end{array}\right|$$=\left|\begin{array}{l}b(b-a)b-cc(b-a)\\ a(b-a)a-bb(b-a)\\ c(b-a)c-aa(b-a)\end{array}\right|$

$={(b-a)}^2\left|\begin{array}{l}bb-cc\\ aa-bb\\ cc-aa\end{array}\right|$

                                                         $\left[\text{on taking }(b-a)\text{ common }{C}_1\text{ and }{C}_3\text{ each}\right]$

$={(b-a)}^2\left|\begin{array}{l}b-cb-cc\\ a-ba-bb\\ c-ac-aa\end{array}\right|$

                                                                 $\left[\because C_1\to C_1-C_3\right]$

$=0$

$\left[\text{since two columns }{C}_1\text{ and }{C}_2\text{ are identical ,so the value of determinant is zero}\right]$