Question

Prove that $[a,b+c,d]=\left[abd\right]+\left[acd\right]$

Answer 1

$\left[a.b+c.d\right]$

$=a.\left\{\right(b+c)\times d\}$

$=\{a.(b+c\left)\right\}\times (a.d)$

$=(a.b+a.c)\times (a.d)$

$=a.b\times (a.d)+a.c\times (a.d)$

$=a.(b\times d)+a.(c\times d)$

$=\left[abd\right]+\left[acd\right]$