Answer
$3z^{2}+wz-4w^{2}$
Work Step by Step
We are given the expression $(z-w)(3z+4w)$. We can find the product of this expression using the FOIL method.
First terms: $z\times 3z=3z^{2}$
Outer terms: $z\times4w=4wz$
Inner terms: $-w\times 3z=-3wz$
Last terms: $-w\times4w=-4w^{2}$
Adding together: $3z^{2}+4wz+(-3wz)+(-4w^{2})=3z^{2}+4wz-3wz-4w^{2}=3z^{2}+wz-4w^{2}$