ANSWER
[tex]3a^{3}bc+6a^{2}b^{3}c[/tex]EXPLANATION
1. We want to expand the expression given:
[tex](abc)(3a^2+6ab^2)[/tex]To do this, use the term in the first bracket to multiply each of the terms in the second bracket and then, simplify:
[tex](abc)(3a^2)+(abc)(6ab^2)[/tex]Now, simplify by multiplying the common terms in each product:
[tex]\begin{gathered} (3*(a^2*a)*b*c)+(6*(a*a)*(b^2*b)*c) \\ \\ 3a^3bc+6a^2b^3c \end{gathered}[/tex]That is the answer.