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

Question

How do you simplify
`(2)/(5) (x+3)x^{(5)/(2) } -2(x+3)x^{(3)/(2) }` into
`(2)/(5) (x-2)(x+3)^{(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.