Explain how you can prove the difference of two cubes identity. a3 - b3 = (a - b) (a2 + ab + b2)

There isn't anything you can do with the left side of the equation. work on the right side instead:

(a-b) (a²+ab+b²)

use distributive property to expand the expression:

a multiple every term in the second parenthesis: a³+a²b+ab²

-b multiple every term in the second parenthesis: - a²b-ab²-b³

add up: (a³+a²b+ab²) + (-a²b-ab²-b³) = a³-b³=the left side