因式分解:one.4a^2b^2-(a^2+b^2)^2〃two.x^4-x^2+8x-16〃three.ab-5b^2-(a+b)(b-a)

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

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

=-(a+b)?(a-b)?

x^4-x^2+8x-16

=x^4-(x^2-8x+16)

=x^4-(x-4)^2

=(x^2+x-4)(x^2-x+4)

有理数范围里已不能分解

=(x^2+x+1/4-4-1/4)(x^2-x+4)

=[(x+1/2)^2-17/4)(x^2-x+4)

=(x+1/2+√17/2)(x+1/2-√17/2)(x^2-x+4)

实数范围里已不能分解

=(x+1/2+√17/2)(x+1/2-√17/2)(x^2-x+1/4+4-1/4)

=(x+1/2+√17/2)(x+1/2-√17/2)[(x-1/2)^2+15/4)

=(x+1/2+√17/2)(x+1/2-√17/2)(x+1/2+√15i/2)(x+1/2-√15i/2)

ab-5b^2-(a+b)(b-a)

=ab-5b^2+a^2-b^2

=a^2+ab-6b^2

=(a+3b)(a-2b)