Question

Multiply:
[−3d + (−7f)] by (5d + f)

Answer 1

To multiply, we will use distributive law as follows:

\[\left[ - 3d + \left( - 7f \right) \right]\left( 5d + f \right)\]

\[ = \left( - 3d \right)\left( 5d + f \right) + \left( - 7f \right)\left( 5d + f \right)\]

\[ = \left( - 15 d^2 - 3df \right) + \left( - 35df - 7 f^2 \right)\]

\[ = - 15 d^2 - 3df - 35df - 7 f^2 \]

\[ = - 15 d^2 - 38df - 7 f^2 \]

Thus, the answer is \[- 15 d^2 - 38df - 7 f^2\].