$\begin{array}{l} a)\sqrt {9{a^3}} + 4{a^2}\\ = \sqrt {{{\left( {3a} \right)}^2}.a} + 4{a^2}\\ = \left| {3a} \right|\sqrt a + 4{a^2}\\ = - 3a\sqrt a + 4{a^2}\\ b)\dfrac{{\sqrt {{a^2} + 2a + 1} }}{{\left| a \right| - 1}}\\ = \dfrac{{\sqrt {{{\left( {a + 1} \right)}^2}} }}{{\left| a \right| - 1}} = \dfrac{{\left| {a + 1} \right|}}{{\left| a \right| - 1}}\\ = \dfrac{{ - 1 - a}}{{ - a - 1}} = 1\left( { - 1 \le a \le 0} \right) \end{array}$