The polynomial describing the total number of leaves on the tree is the product of the two models. This is like multiplying the number of branches by the number of trees. If t(y)t(y) represents the total number of leaves on the tree, we write:

\(\displaystyle{t}{\left({y}\right)}={b}{\left({y}\right)}⋅{l}{\left({y}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={\left({4}{y}^{{2}}+{y}\right)}{\left({2}{y}^{{3}}+{3}{y}^{{2}}+{y}\right)}\)

Use distributive property:

\(\displaystyle{t}{\left({y}\right)}={2}{y}^{{3}}{\left({4}{y}^{{2}}+{y}\right)}+{3}{y}^{{2}}{\left({4}{y}^{{2}}+{y}\right)}+{y}{\left({4}{y}^{{2}}+{y}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={\left({8}{y}^{{5}}+{2}{y}^{{4}}\right)}+{\left({12}{y}^{{4}}+{3}{y}^{{3}}\right)}+{\left({4}{y}^{{3}}+{y}^{{2}}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={8}{y}^{{5}}+{14}{y}^{{4}}+{7}{y}{3}+{y}^{{2}}\)

\(\displaystyle{t}{\left({y}\right)}={b}{\left({y}\right)}⋅{l}{\left({y}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={\left({4}{y}^{{2}}+{y}\right)}{\left({2}{y}^{{3}}+{3}{y}^{{2}}+{y}\right)}\)

Use distributive property:

\(\displaystyle{t}{\left({y}\right)}={2}{y}^{{3}}{\left({4}{y}^{{2}}+{y}\right)}+{3}{y}^{{2}}{\left({4}{y}^{{2}}+{y}\right)}+{y}{\left({4}{y}^{{2}}+{y}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={\left({8}{y}^{{5}}+{2}{y}^{{4}}\right)}+{\left({12}{y}^{{4}}+{3}{y}^{{3}}\right)}+{\left({4}{y}^{{3}}+{y}^{{2}}\right)}\)

\(\displaystyle{t}{\left({y}\right)}={8}{y}^{{5}}+{14}{y}^{{4}}+{7}{y}{3}+{y}^{{2}}\)