Prove the following identities :
(i)(a+b)3=a3+b3+3a2b+3b2a
(ii)(a−b)3=a3−b3−3a2b+3b2a [4 MARKS]
Application: 2 Marks each
(i)(a+b)3=(a+b)2(a+b)
=(a2+b2+2ab)(a+b)
=a3+a2b+ab2+b3+2a2b+2ab2
=a3+b3+3a2b+3ab2
(ii)(a−b)3=(a−b)2(a−b)
=(a2+b2−2ab)(a−b)
=a3−a2b+ab2−b3−2a2b+2ab2
=a3−b3−3a2b+3ab2