Question

（a^2+b^2)^2-4a^2b^2 分解因式

Answer 1

因为
a^2+b^2-4a^2b^2
=a^2+b^2-4a^2b^2+2ab-2ab
=(a+b)^2-4a^2b^2-2ab
=(a+b)^2-4a^2b^2-2ab+1/4-1/4
=(a+b)^2-(2ab+1/2)^2+1/4
=(a+b+2ab+1/2)(a+b-2ab-1/2)+1/4
所以
4a^2b^2-(a^2+b^2)
=-(a+b+2ab+1/2)(a+b-2ab-1/2)-1/4
如果原题错了，应该为(a^2+b^2-c^2)^2-4a^2b^2
则解答为:
(a^2+b^2-c^2)^2-4a^2b^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+b)^2-c^2][(a-b)^2-c^2]
=(a+b+c)(a+b-c)(a-b+c)(a-b-c)
如果原题为(a^2+b^2)^2-4a^2b^2
则解答为:
(a^2+b^2)^2-4a^2b^2
=(a^4+2a^2b^2+b^4)-4a^2b^2
=(a^4-2a^2b^2+b^4)
=(a^2-b^2)^2
=(a-b)^2(a+b)^2
祝你学习天天向上，加油!!!!!!!!!!!!

Answer 2

（a^2+b^2)^2-4a^2b^2 =(a^2)^2+2a^2*b^2+(b^2)^2-4a^2b^2=(a^2)^2-2a^2*b^2+(b^2)^2=(a^2-b^2)^2

Answer 3

a^2+b^2-4a^2b^2
=a^2+b^2-4a^2b^2+2ab-2ab
=(a+b)^2-4a^2b^2-2ab
=(a+b)^2-4a^2b^2-2ab+1/4-1/4
=(a+b)^2-(2ab+1/2)^2+1/4
=(a+b+2ab+1/2)(a+b-2ab-1/2)+1/4

Answer 4

（a^2+b^2)^2-4a^2b^2
=（a^2+b^2)^2-(2ab)^2
=(a^2+2ab+b^2)(a^2-2ab+b^2)
=(a+b)^2(a-b)^2

Answer 5

(a+b)^2(a-b)^2