a4+b4+c4-a2b2-b2c2-a2c2

= 1/2×2×(a4+B4+C4-a2 B2-B2 C2-a2 C2)

= 1/2×(2 a4+2 B4+2 C4-2a2b 2-2b2c 2-2a2c 2)

= 1/2×[(a4-2a2b 2+B4)+(a4-2b2c 2+C4)+(B4-2a2c 2+C4)]

= 1/2×[(a2-B2)2+(a2-C2)2+(B2-C2)2]

It can be changed to1/2× [(A2-B2) 2+(A2-C2) 2+(B2-C2) 2].

PS。 The final answer can be separated from parentheses.

It is1/2 (A2-B2) 2+1/2 (A2-C2) 2+1/2 (B2-C2) 2.