Đáp án:
`(a-b-c).(a-b+c).(a+b-c).(a+b+c)`
Giải thích các bước giải:
`a^4+b^4+c^4-2a^2 b^2 -2b^2 c^2 -2a^2 c^2`
`=a^4+b^4+c^4+2a^2 b^2-4a^2 b^2 -2b^2 c^2 -2a^2 c^2`
`=(a^4 +2a^2 b^2 +b^4)+(-2b^2 c^2 - 2a^2 c^2 )+c^4-4a^2 b^2`
`=[(a^2)^2 +2a^2 b^2 +(b^2)^2 ]-2.(a^2 +b^2 ).c^2 +c^4 -4a^2 b^2`
`=(a^2+b^2)^2 -2.(a^2 +b^2) .c^2 +(c^2)^2 -4a^2 b^2`
`=[(a^2+b^2)-c^2]^2-4a^2 b^2`
`=(a^2 +b^2 -c^2)^2-(2ab)^2`
`=(a^2 +b^2-c^2 -2ab).(a^2+b^2-c^2 +2ab)`
`=[(a^2-2ab+b^2)-c^2].[(a^2+2ab+b^2)-c^2]`
`=[(a-b)^2-c^2].[(a+b)^2-c^2]`
`=(a-b-c).(a-b+c).(a+b-c).(a+b+c)`