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Question

Prove the following identities :

(i)(a+b)3=a3+b3+3a2b+3b2a

(ii)(ab)3=a3b33a2b+3b2a [4 MARKS]


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Solution

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)(ab)3=(ab)2(ab)

=(a2+b22ab)(ab)

=a3a2b+ab2b32a2b+2ab2

=a3b33a2b+3ab2


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