Question

a^4+b^4+c^4-2a^2b^2-2b^2c^2-2c^2a^2因式分解

Answer 1

原式=(a^4-2a²b²+b^4)+2a²c²-2b²c²+c^4-4a²c²
=(a²-b²)²+2c²(a²-b²)+c&4-4a²c²
=(a²-b²+c²)²-4a²c²
=(a²-b²+c²+2ac)(a²-b²+c²-2ac)
=[(a+c)²-b²][(a-c)²-b²]
=(a-b+c)(a+b+c)(a-b-c)(a+b-c)

Answer 2

a^4+b^4+c^4-2a^2b^2-2b^2c^2-2c^2a^2
=a^4+b^4+c^4+2a^2b^2-2b^2c^2-2c^2a^2-4a^2b^2
=(a2+b2-c2)^2-(2ab)^2
=(a2+b2+2ab-c2)(a2+b2-2ab-c2)
=[(a+b)^2-c^2][(a-b)^2-c^2]
=(a+b+c)(a+b-c)(a-b+c)(a-b-c)