Answer
$3x^{3}(x+3)^{2}(x^{2}-5)$
Work Step by Step
$3x^{3}(x^{2}+3x)^{2}-15x(x^{2}+3x)^{2}$
... factor x out of $x^{2}+3x$
$= 3x^{3}[x\cdot(x+3)]^{2}-15x[x\cdot(x+3)]^{2}$
....... apply $(ab)^{m}=a^{m} b^{m}$ on $[x\cdot(x+3)]^{2}$
$= 3x^{3}\cdot x^{2}\cdot(x+3)^{2}-15x\cdot x^{2}\cdot(x+3)^{2}$
$= 3x^{5}\cdot(x+3)^{2}-15x^{3}\cdot(x+3)^{2}$
greatest common factor=$3x^{3}(x+3)^{2}$
$= x^{2}\cdot[3x^{3}(x+3)^{2}]-5\cdot[3x^{3}(x+3)^{2}]$
factor out the term $[3x^{3}(x+3)^{2}]$
$=3x^{3}(x+3)^{2}(x^{2}-5)$
