Question

Show that A vector +B vector cross A vector-B vector =2(B vector cross A vector)

Answer 1

(A+B)x(A-B)= (A+B)xA-(A+B)xB=AxA+BxA-AxB-BxB=0+BxA-AxB-0=2(BxA) .
Note:Vector product is distributive but not commutative