Resolve each of the following quadratic trinomial into factor:

The given expression is $15 x^{2}-16 x y z-15 y^{2} z^{2}$.             (Coefficient of $x^{2}=15$, coefficient of $x=-16 y z$ and constant term $=-15 y^{2} z^{2}$ )

Now, we will split the coefficient of $x$ into two parts such that their sum is $-16 y z$ and their product equals the product of the coefficient of $x^{2}$ and the cons $\tan t$ term, i.e., $15 \times\left(-15 y^{2} z^{2}\right)=-225 y^{2} z^{2}$.

Now,

$(-25 y z)+9 y z=-16 y x$

and

$(-25 y z) \times 9 y z=-225 y^{2} z^{2}$

Replacing the middle term $-16 x y z$ by $-25 x y z+9 x y z$, we have :

$15 x^{2}-16 x y z-15 y^{2} z^{2}=15 x^{2}-25 x y z+9 x y z-15 y^{2} z^{2}$

$=\left(15 x^{2}-25 x y z\right)+\left(9 x y z-15 y^{2} z^{2}\right)$

$=5 x(3 x-5 y z)+3 y z(3 x-5 y z)$

$=(5 x+3 y z)(3 x-5 y z)$