Prove that: a^3-b^3=(a-b)(a^2-ab+b^2)?

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We have to prove that a^3 - b^3 = (a - b)(a^2 - ab + b^2)

This is not the right factorization a^3 - b^3 = (a - b)(a^2 + ab + b^2)

To prove this start with the right hand side

(a - b)(a^2 + ab + b^2)

=> a*(a^2 + ab + b^2) - b*(a^2 + ab + b^2)

=> a^3 + a^2*b + a*b^2 - a^2*b - a*b^2 - b^3

=> a^3 + a^2*b - a^2*b + a*b^2 - a*b^2 - b^3

=> a^3 - b^3

This proves that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

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