Special Products Rule 6

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Expand $(4p + q)(16p^{2} - 4pq +q^{2})$

**Answer**

$\;\;\;(4p + q)(16p^{2} - 4pq +q^{2})$

$=(4p + q)((4p)^2 - (4p)(q) + (q)^2) $

$=(A + B)(A^2 - AB + B^2) \text{ , where } A = 4p \text{ and } B = q $

$=A^3 + B^3 $

$=(4p)^3 + (q)^3 $

$=64p^{3} + q^{3} $