Question

Please help!!
(a - b)(a^2 + ab + b^2)
It should be solved using FOIL

Answer 1

Use the distributive property (of which the FOIL method is a special case):

(a - b) (a² + ab + b²)

= (a - b) a² + (a - b) ab + (a - b) b²

= (a³ - a²b) + (a²b - ab²) + (ab² - b³)

= a³ - b³

Alternatively, you can distribute the quadratic expression over each term in a - b :

(a - b) (a² + ab + b²)

= a (a² + ab + b²) - b (a² + ab + b²)

= (a³ + a²b + ab²) - (a²b + ab² + b³)

= a³ - b³