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

Question

asked Jul 17, 2021 72.4k views

1 Answer

Franklinsijo · Answer 1 · 2021-07-23T11:30:33+0000

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.