I'm trying to prove equation (1.35)

> 
> $$\begin{align}
>  (\mathbf{a}\times\mathbf{b})^2 &=
>  \mathbf{a}^2\mathbf{b}^2 - (\mathbf{a}\cdot\mathbf{b})^2 \\
>  &− a\_j[a\_j,b\_k]b\_k + a\_j[a\_k,b\_k]b\_j − a\_j[a\_k,b\_j]b\_k − a\_ja\_k[b\_k,b\_j]
> \end{align} \tag{1.35}$$
> 
> 
> 

of lecture note ["*Angular Momentum*"](https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) by B. Zwiebach
from ["*MIT OpenCourseWare - Physics - Quantum Physics II (fall 2013) - Lecture Notes*"](https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/)
in order to apply it later to the operators $\vec{L}^2$, $\vec{r}$ and $\vec{p}$, but I can't arrive to that relation. How would you adress it? Thank you