Question

( a^{3}-b^{3}=(a-b)left(a^{2}+a b+b^{2}right) )
you know that
( (a-b)^{3}=a^{3}+3 a b(a-b)-b^{3} )
then ( a^{3}-b^{3}=(a-b)^{3}+3 a b(a-b) )
( =(a-b)left[(a-b)^{2}+3 a bright] )
( =(a-b)left(a^{2}-2 a b+b^{2}+3 a bright) )
( =(a-b)left(a^{2}+a b+b^{2}right) )

# If AB + BA = 0, then prove that A3 --B3 = (A + B) (AP - AB-B4). D2

Solution