Multiply: [−3d + (−7f)] by (5d + f)

To multiply, we will use distributive law as follows:

[−3d + (−7f)] by (5d + f)

$=(-3 d)(5 d+f)+(-7 f)(5 d+f)$

$=\left(-15 d^{2}-3 d f\right)+\left(-35 d f-7 f^{2}\right)$

$=-15 d^{2}-3 d f-35 d f-7 f^{2}$

$=-15 d^{2}-38 d f-7 f^{2}$

Thus, the answer is $-15 d^{2}-38 d f-7 f^{2}$.