(a-b)(a^2ab+b^2)

(a-b)(a^2ab+b^2)

Input
(a – b) (a^2 a b + b^2)
Result
(a – b) (a^3 b + b^2)
Expanded form
a^4 b – a^3 b^2 + a b^2 – b^3
Alternate form assuming a and b are positive
b (a^4 – a^3 b + a b – b^2)
Real root
b = 0
Polynomial discriminant
Delta_a = -27 b^6 (b^4 + b^2)^2
Property as a function
odd
Derivative
(d)/(da)((a – b) (a^2 a b + b^2)) = b (4 a^3 – 3 a^2 b + b)
Indefinite integral
integral (a – b) (a^3 b + b^2) da = b (a^5/5 – (a^4 b)/4 + (a^2 b)/2 – a b^2) + constant

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