Factor ac^2 - a^3 - a^2b + ab^2 + b^3 - bc^2

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Question from erson, a student:

help me with this...please....

factorize:
ac^2 - a^3 - a^2b + ab^2 + b^3 - bc^2

thanks....
i hope i'll get this as soon as possible...
thanks.

Erson,

I can get you started. If you collect the terms you can see a common factor of a - b.

ac² - a³ - a²b + ab² + b³ - bc²
= [ac² - bc²] + [ab² - a²b] + [b³ - a³]
= c²(a - b) + ab(b - a) + (b - a)(b² + ba + a²)

Can you complete it from here?

Harley

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