B3 Simplify the expression $(x+2)^{2}-(x-2)(x+2)-4 x^{2}+\frac{2}{x}$ and accurately calculate the value of the expression for $x=\sqrt{2}$. Rationalize the result.
B3. Squaring $(x+2)^{2}=x^{2}+4 x+4$. Organizing the second term of the expression $(x-2)(x+2)=x^{2}-4$. Considering the negative sign before the second term, we get $x^{2}+4 x+4-x^{2}+4-4 x^{2}+\frac{2}{x}$. Organizing $-4 x^{2}+8+4 x+\frac{2}{x}$. Substituting $x=\sqrt{2}$, we get $-4 \sqrt{2}^{2}+8+4 \sqrt{2}+\frac{2}{\sqrt{2}}$. Rationalizing the last term $\frac{2 \sqrt{2}}{2}$. We get the result $5 \sqrt{2}$.
Squaring $(x+2)^{2}=x^{2}+4 x+4$ ..... 1 point
Organizing the second term $(x-2)(x+2)=x^{2}-4$ ..... 1 point
Organizing the expression $-4 x^{2}+8+4 x+\frac{2}{x}$ ..... 1 point
Substituting $x=\sqrt{2}$ ..... 1 point
Rationalizing the denominator ..... 1 point
Solution $5 \sqrt{2}$ ..... 1 point