The given simplification is not correct. This one is:
[tex]\displaystyle \frac25 (x + 3) x^{5/2} - 2 (x+3) x^{3/2} = \frac25 (x+3) x^{3/2} \bigg(x^{2/2} - 5\bigg) = \frac25 (x+3) x^{3/2} (x - 5)[/tex]
which is just a matter of recognizing [tex]2(x+3)x^{3/2}[/tex] as a common factor to both expressions in the sum.
