find the product of (a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]
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Step-by-step explanation:
=(a+b+c)[a²+b²-2ab+b²+c²-2bc+c²+a²-2ac]
=(a+b+c)[2a²+2b²+2c²-2ab-2bc-2ac]
=a[2a²+2b²+2c²-2ab-2bc-2ac]+b[2a²+2b²+2c²-2ab-2bc-2ac]+c[2a²+2b²+2c²-2ab-2bc-2ac]
=2a³+2ab²+2ac²-2a²b-2abc-2a²c+2a²b+2b³+2bc²-2ab²-2cb²-2abc+2a²c+2cb²+2c³-2abc-2bc²-2ac²
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