What is the formula for (a3 - b3)?

Answer: 

(a3 – b3) = (a – b)(a2 + b2 + ab)

Let us prove this by considering a = 4 and b= 2 then

(43 – 23) = (4 – 2)(42 + 22 + 4 × 2)

LHS = (2)(28)

LHS = 56

RHS = (a – b)(a2 + b2 + ab)

RHS = (4 – 2)(42 + 22 + 4 × 2)

RHS = 56

∴ LHS = RHS

(a3 – b3) = (a – b)(a2 + b2 + ab)

Hence the proof.

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