Question

what is the formula for (a3-b3).

Answer 1

We can derive the above using identity (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

Answer 2

Answer:

a3-b3=(a-b)(a2+ab+b2)