Multiply: [-3 d+(-7 f)] by (5 d+f) - Vidyadip

Question

Multiply:
$[-3 d+(-7 f)] \text { by }(5 d+f)$

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Answer

To multiply, we will use distributive law as follows:
${[-3 d+(-7 f)](5 d+f)}$
$=(-3 d)(5 d+f)+(-7 f)(5 d+f)$
$=\left(-15 d^2-3 d f\right)+\left(-35 d f-7 f^2\right)$
$=-15 d^2-3 d f-35 d f-7 f^2$
$=-15 d^2-38 d f-7 f^2$
Thus, the answer is $-15 d^2-38 d f-7 f^2$.

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