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## Homework Statement

[itex]A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\quad =\quad ?[/itex]

## Homework Equations

Various cross product and dot product properties

## The Attempt at a Solution

I've only managed to get so far, don't really know what to do next

[itex]A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\\ \\ =(2A+B)\quad \cdot \quad [(A-C)\times 2B\quad +\quad (A-C)\times C]\\ =(2A+B)\quad \cdot \quad [A\times 2B\quad -\quad C\times 2B\quad +\quad A\times C][/itex]