计算(a+b+c)^2+(a+b-c)^2+(a-b+c)^2+(b-a+c)^2,
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计算(a+b+c)^2+(a+b-c)^2+(a-b+c)^2+(b-a+c)^2,
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(a+b+c)^2+(a+b-c)^2+(a-b+c)^2+(b-a+c)^2
=(a+b)²+2c(a+b)+c²+(a+b)²-2c(a+b)+c²+(a-b)²+2c(a-b)+c²+(b-a)²+2c(b-a)+c²
=a²+2ab+b²+4c²+a²+2ab+b²+a²-2ab+b²+b²-2ab+b²
=4a²+4b²+4c²
=(a+b)²+2c(a+b)+c²+(a+b)²-2c(a+b)+c²+(a-b)²+2c(a-b)+c²+(b-a)²+2c(b-a)+c²
=a²+2ab+b²+4c²+a²+2ab+b²+a²-2ab+b²+b²-2ab+b²
=4a²+4b²+4c²
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