Multiply the following polynomials
$(5 - d^{2} + 2 d) (2 d - 1)$

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Solution

Multiplying each term of the first with each term of the second and adding gives:
$5 \cdot 2 d + 5 \cdot - 1 + - d^{2} \cdot 2 d + - d^{2} \cdot - 1 + 2 d \cdot 2 d + 2 d \cdot - 1$
$= 10 d - 5 - 2 d^{3} + d^{2} + 4 d^{2} - 2 d$
$= - 2 d^{3} + 5 d^{2} + 8 d - 5$

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