<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] $$(\mathbf a+2\mathbf b)\cdot(2\mathbf a-\mathbf b)=2\mathbf a\mathbf a-\mathbf a\mathbf b+4\mathbf b\mathbf a-2\mathbf b\mathbf b=2(|\mathbf a|^2-|\mathbf b|^2)+3\mathbf a\mathbf b$$
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