What is the formula for (a3 – b3)?

Answer:

(a³ – b³) = (a – b)(a² + b² + ab)

Let us prove this by consider a = 5 and b= 3 then

(5³ – 3³) = (5 – 3)(5² + 3² + 5 × 3)

LHS = (125 – 27)

LHS = 98

RHS = (a – b)(a² + b² + ab)

RHS = (5 – 3)(5² + 3² + 5 × 3)

RHS = (2) X (25 + 9 + 5 × 3)

RHS = (2) X (34 + 15)

RHS = 2 X 49

RHS = 98

∴ LHS = RHS

(a³ – b³) = (a – b)(a² + b² + ab)

Hence Proved

What is the importance of the a cube – b cube formula?