证明题;也只a+2b=0,求正：a^3+2ab(a+b)+4b^3=0

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证明：a^3+2ab(a+b)+4b^3
=a^3+2a^2b+2ab^2+4b^3
=a^2(a+2b )+2b^2(a+2b)
=a^2*0+2b^2*0
=0

a^3+2ab(a+b)+4b^3
=a^3+2a^2b+2ab^2+4b^3
=a^2(a+2b)+2b^2(a+2b)
=(a+2b)*(a^2+2b^2)
=0*(a^2+2b^2)
=0