Question

How do I factor (x^2+4)^3/2 - x^2(x^2+4)^-1/2 ?

Answer 1

Hello,

$(x^2+4)^{3/2} - x^2(x^2+4)^{-1/2}\\\\ =(x^2+4) \sqrt{x^2+4} - \dfrac{x^2}{\sqrt{x^2+4}} \\\\ =\dfrac{1}{\sqrt{x^2+4}}((x^2+4)^2-x^2)\\\\ =\dfrac{(x^2-x+4)(x^2+x+4)}{\sqrt{x^2+4}}$