<s>[INST] Simplify the Dot Product in terms of $a$ and $b$ Where $a$ and $b$ are arbitrary vectors
$(a+2b) \cdot (2a-b)$
$$a\cdot(2a-b)+2b\cdot(2a-b) = 2(a\cdot a)-a\cdot b+1(b\cdot a)-2(b\cdot b)$$
$$=2(a)-ab+4ab-2(b)^2$$
$$=2a^2-2b^2$$
$$=2(a^2-b^2)$$
Where did i go wrong in simplifying this?
 [/INST] I marked the mistakes in red and corrected these
\begin{align}
(a+2b) * (2a-b)& =a*(2a-b)+2b*(2a-b)\\
& = 2(a*a)-a*b+\color{red}{4}(b*a)-2(b*b)\\
& = 2(a)\color{red}{^2}\underbrace{-ab+4ab}_{\color{red}{3ab}}-2(b)^2\\
& = 2a^2-2b^2+\color{red}{3ab}\\
& = 2(a^2-b^2)+\color{red}{3ab}
\end{align}
</s>