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14-12-2020
Mathematics

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How would you factor a^3 - b^3? Please leave detailed instructions. Thanks so much!

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LammettHash LammettHash

14-12-2020

a³ - b³ = (a - b) (a² + ab + b²)

You can see why this works if you expand the right side as

a (a² + ab + b²) - b (a² + ab + b²)

(a³ + a²b + ab²) - (a²b + ab² + b³)

Both the a²b and ab² terms cancel, leaving you with a³ - b³.

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