#### Answer

$(3p-1)(9p^{2}+3p+1)=27p^{3}-1$

#### Work Step by Step

$(3p-1)(9p^{2}+3p+1)$
Evaluate the product indicated by multiplying the first term and second term of the first factor by every element in the second factor separately:
$(3p-1)(9p^{2}+3p+1)=...$
$...=27p^{3}+9p^{2}+3p-9p^{2}-3p-1=...$
Simplify:
$...=27p^{3}-1$