Question

因式分解4a平方b平方-a四次方-b四次方-c四次方-2（a平方b平方-a平方c平方-b平方c平方）

Answer 1

4a^2b^2-a^4-b^4-c^4-2(a^2b^2-a^2c^2-b^2c^2)
=4a^2b^2-a^4-b^4-c^4-2a^2b^2+2a^2c^2+2b^2c^2
=2a^2b^2+2a^2c^2+2b^2c^2-a^4-b^4-c^4
=-[a^4+b^4+c^4-2a^2b^2-2a^2c^2-2b^2c^2 ]
=-(a^4-2a^2b^2+b^4)-2a^2c^2+2b^2c^2+c^4-4b^2c^2
=-(a^2-b^2)^2-2c^2(a^2-b^2)+c^4-4b^2c^2
=-(a^2-b^2-c^2)^2-4b^2c^2
=-(a^2-b^2-c^2+2bc)(a^2-b^2-c^2-2bc)
=-[a^2-(b^2-2bc+c^2)][a^2-(b^2＋2bc＋c^2)]
=-[a^2-(b－c)^2][a^2-(b＋c)^2]
=(c-a-b)(a-b+c)(a+b+c)(a-b-c)