Question

a2+b2=ab
(a3/b3)+(b3/b3)=?​

Answer 1

Answer:

Let us derive it by using identity (a−b)3(a−b)3

(a−b)3=a3−3a2b+3ab2−b3(a−b)3=a3−3a2b+3ab2−b3

(a−b)3=a3−3ab(a−b)−b3(a−b)3=a3−3ab(a−b)−b3

(a−b)3+3ab(a−b)=a3−b3(a−b)3+3ab(a−b)=a3−b3

(a−b)[(a−b)2+3ab]=a3−b3(a−b)[(a−b)2+3ab]=a3−b3

(a−b)[a2−2ab+b2+3ab]=a3−b3(a−b)[a2−2ab+b2+3ab]=a3−b3

(a−b)[a2+ab+b2]=a3−b3

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