Another method is to do the polynomial long division:
[HTML] a^2 + ab + b^2
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a - b )a^3 + 0a^2b + 0ab^2 - b^3
a^3 - 1a^2b
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1a^2b + 0ab^2 - b^3
1a^2b - 1ab^2
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1ab^2 - b^3
1ab^2 - b^3
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0[/HTML]