Simplify this simple expression?

Question

So the expression is $-(1/3)(1/2)^{3/2} + 1/3 - (1/3)(1/\sqrt{2})^3$.

The answer in my book is $1/3(1 - 1/\sqrt{2})$. But that simplifies to $1/3 - 1/3\sqrt{2}$. How come it isn't $1/3 + 2(-1/\sqrt{2})$, which is what I got.

Answer 1

$ −\frac 13(\frac 12)^{\frac 32}+\frac 13 −\frac 13(\frac 1{\sqrt 2})^3=$

$\frac 13[-(\frac 12)^{\frac 32}+1 - (\frac 1{\sqrt 2})^3]=$

$\frac 13[-(\frac 12)^{\frac 32}+1 - (\frac 1{2})^{\frac 32}]=$

$\frac 13[1 - 2*(\frac 1{2})^{\frac 32}]=$

$\frac 13[1 - 2*(\frac 1{2})^{1+\frac 12}]=$

$\frac 13[1 - 2*(\frac 1{2})^{1}(\frac 12)^{\frac 12}]=$

$\frac 13[1- \frac 12^{\frac 12}]=$

$\frac 13 - \frac 1{3\sqrt 2}$