Đáp án:
`a)-a²-b²-c²`
`b)4a²+4b²+4c²`
Giải thích các bước giải:
`a)(a+b+c)²-(a+b)²-(a+c)²-(b+c)²`
`=[(a+b)+c]²-(a²+2ab+b²)-(a²+2ac+c²)-(b²+2bc+c²)`
`=(a+b)²+2c(a+b)+c²-a²-2ab-b²-a²-2ac-c²-b²-2bc-c²`
`=a²+2ab+b²+2ac+2bc+c²-a²-2ab-b²-a²-2ac-c²-b²-2bc-c²`
`=(a²-a²-a²)+(2ab-2ab)+(b²-b²-b²)+(2ac-2ac)+(2bc-2bc)+(c²-c²-c²)`
`=-a²-b²-c²`
`b)(a+b+c)²+(a-b+c)²+(a+b-c)²+(-a+b+c)²`
`=[(a+b)+c]²+[(a-b)+c]²+[(a+b)-c]²+[c-(a-b)]²`
`=(a+b)²+2c(a+b)+c²+(a-b)²+2c(a-b)+c²+(a+b)²-2c(a+b)+c²+c²-2c(a-b)+(a-b)²`
`=[(a+b)²+(a+b)²]+[2c(a+b)-2c(a+b)]+(c²+c²+c²+c²)+[(a-b)²+(a-b)²]+[2c(a-b)-2c(a-b)]`
`=2(a+b)²+4c²+2(a-b²)`
`=2[(a+b)²+2c²+(a-b)²]`
`=2(a²+2ab+b²+2c²+a²-2ab+b²)`
`=2[(a²+a²)+(2ab-2ab)+(b²+b²)+2c²]`
`=2(2a²+2b²+2c²)`
`=4a²+4b²+4c²`
