First lets solve the first part.
(a + b) (a - b) = a² - ab
+ ab - b²
= a² - b² (the - ab and the + ab cancel each other out)
Now lets solve:
(a² - b²) (a + b) = a³ + a²b - ab² - b³
Finally, use this and solve:
(a³ + a²b - ab² - b³) (a - b)
=

- a³b + a³b - a²b² - a²b² + ab³ - ab³ +

=
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- 2a²b² +