We multiply the polynomials by using the terms from ${a-3b}$ successively. $$\begin{aligned} \left({a-3b}\right)\left({a^{2}+7ab+9b^{2}}\right)&= {aa^{2}+a\cdot 7ab+a\cdot 9b^{2}-3ba^{2}-3b\cdot 7ab-3b\cdot 9b^{2}}\\ & = {a^{3}+4a^{2}b-12ab^{2}-27b^{3}} \end{aligned}$$