Special Products Rule 4

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Expand $(2p + q)^3 $

**Answer**

$\;\;\;(2p + q)^3 $

$=(A + B)^3 \text{ , where } A = 2p \text{ and } B= q$

$=A^3 + 3A^2B + 3AB^2 + B^3 $

$=(2p)^3 + 3(2p)^2(q) + 3(2p)(q)^2 + (q)^3 $

$= 8p^{3} + 3(4p^{2})(q) + 3(2p)(q^{2}) + q^{3} $

$= 8p^{3} + 12p^{2}q + 6pq^{2} + q^{3} $