Hi, the problem is to factor and simplify the expression

$\displaystyle (x^2-4)(x^2+3)^{1/2} - (x^2-4)^2(x^2+3)^{3/2}$

I can factor the left side but the right leaves me stuck.

I tried multiplying both terms in the right and got $\displaystyle (x^4-8x^2+16) \sqrt{x^6+9x^4+27x^2+27}$

but I feel like I am going the wrong way and don't think it should be this complicated.

The answer in the back of the book is $\displaystyle (x+2)(x-2)(x^2+3)^{1/2}(-x^4 +x^2 +13)$

I don't know where the final term came from.

Thank you.