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Question
Multiply:
[−3d + (−7f)] by (5d + f)
Solution
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 \[- 15 d^2 - 38df - 7 f^2\].
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