Question

x^4-2(a^2+b^2)x^2+(a^2-b^2)2,因式分解,

Answer 1

x^4-2(a^2+b^2)x^2+(a^2-b^2)2 =x^4-2(a^2+b^2)x^2+(a^2-b^2)2+4a^2b^2- 4a^2b^2 =x^4-2(a^2+b^2)x^2+(a^2+b^2)2- (2ab)^2 =(x^2-a^2-b^21)^2- (2ab)^2 =(x^2-a^2-b^21+2ab)(x^2-a^2-b^21-2ab) =(x^2-(a-b)^2)(x^2-(a+b)^2) =(x-a+b)(x+a-b)(x-a-b)(x+a+b)