Answer
$-x^{3}(x^{3}+1)\sqrt{x+1}$
Work Step by Step
From the two terms, we can factor out
$(x^{3}+1)$ and
$\sqrt{x+1}$
$...=(x^{3}+1)\sqrt{x+1}[1-(x^{3}+1)]$
$=(x^{3}+1)\sqrt{x+1}(-x^{3})$
$=-x^{3}(x^{3}+1)\sqrt{x+1}$
Note:
For $x^{3}+1$ there is a special formula,
the sum of cubes:
$a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
so
$x^{3}+1=(x+1)(x^{2}-x+1)$
The answer could be further factored:
$-x^{3}(x+1)(x^{2}-x+1)\sqrt{x+1}$
but the sum of cubes is not covered in this section,
so we leave the answer as it is.
