I am trying to multiply and simplify the following radical expression.
$$(\sqrt{x}+5 - 4)(\sqrt{x}+5+4)$$
According to the book, the answer is $x - 11$
However, I am confused about how this even works. I tried using the following calculator that shows all the steps. http://www.softmath.com/math-com-calculator/adding-matrices/multiply-radical-expressions.html#c=simplify_algstepssimplify&v217=%2528%25u221Ax%2B5%2520-%25204%2529%2528%2520%25u221Ax%2B5%2B4%2529
However, the answer is completely different when using the calculator $x + 10\sqrt{x} + 9$.
I know I must be missing something here and it is probably something simple. I can simplify radicals by themselves with no problem, but when they are multiplied that is when I get into trouble.
You have: $$(\sqrt{x+5}-4)(\sqrt{x+5}+4)$$ Your lack of collecting the $+5$ under the square root is why your calculator procured the incorrect answer.
Instead, use Difference of Two Squares here: $$(A-B)(A+B)=A^2-B^2$$ (achievable by expanding)