Can anyone help me to proof the 2nd expression? We need to proof these expressions when a and b are real numbers

Here is what I have tried so far


When $a = 0$ and/or $b = 0$, the inequalities clearly hold. Now consider the case $a \neq 0$ and $b \neq 0$.
Both 2) and 3) reduce to 1). For 2), you have
\begin{align}
a^6 + a^4b^2 + a^2b^4 + b^6 &\text{ vs. } a^6 + 2a^3b^3 + b^6, \\
a^4b^2 + a^2b^4 &\text{ vs. }  2a^3b^3,\\
a^2 + b^2 &\text{ vs. }  2ab.
\end{align}
In the final step, you simply divide both sides by $a^2b^2 > 0$.
For 3), you have
\begin{align}
2a^2+2b^2 &\text{ vs. } a^2 + 2ab + b^2, \\
a^2+b^2 &\text{ vs. } 2ab.
\end{align}
Now just do the same as what you did for 1).
