Levi Civita proof - Curl

cristina89

I need to prove that [tex]\nabla \times (\vec{A} \times \vec{B}) [/tex]

Well. Trying to solve it, I've come to this:

[tex]\partial_j \vec{A}_i \vec{B}_j \hat{u}_i- \partial_i \vec{A}_i \vec{B}_j \hat{u}_j [/tex]

Then I've found in my book that this is equal to:

[tex]\vec{A}_i \partial_j \vec{B}_j \hat{u}_i + \partial_j \vec{B}_j \vec{A}_i \hat{u}_i - (\vec{A}_i \partial_i \vec{B}_j \hat{u}_j + \vec{B}_j \vec{A}_i \partial_i \hat{u}_j) [/tex]

Can someone explain to me why?