Answer
$$\frac{A}{{x + 2}} + \frac{B}{{{{\left( {x + 2} \right)}^2}}} + \frac{C}{{{{\left( {x + 2} \right)}^3}}}$$
Work Step by Step
$$\eqalign{
& {\text{Given exercise }}\frac{{{x^2}}}{{{{\left( {x + 2} \right)}^3}}} \cr
& {\text{In the denominator the expression is }}{\left( {x + 2} \right)^3}{\text{ it is a linear}} \cr
& {\text{repeated factor, then the numerator for each term of the}} \cr
& {\text{partial fraction decomposition is a different constant, so }} \cr
& {\text{the decomposition is:}} \cr
& \frac{{{x^2}}}{{{{\left( {x + 2} \right)}^3}}} = \frac{A}{{x + 2}} + \frac{B}{{{{\left( {x + 2} \right)}^2}}} + \frac{C}{{{{\left( {x + 2} \right)}^3}}} \cr} $$
