Question

How do you simplify $\frac{2}{5} (x+3)x^{\frac{5}{2} } -2(x+3)x^{\frac{3}{2} }$ into $\frac{2}{5} (x-2)(x+3)^{\frac{3}{2} }$

Answer 1

The given simplification is not correct. This one is:

$\displaystyle \frac25 (x + 3) x^{5/2} - 2 (x+3) x^{3/2} = \frac25 (x+3) x^{3/2} \bigg(x^{2/2} - 5\bigg) = \frac25 (x+3) x^{3/2} (x - 5)$

which is just a matter of recognizing $2(x+3)x^{3/2}$ as a common factor to both expressions in the sum.