一道实数范围内的分解因式

(x+a)(x+2a)(x+3a)(x+4a)+a^4
=[(x+a)(x+4a)][(x+2a)(x+3a)]+a^4
=[x^2+5ax+4a^2][x^2+5ax+6a^2]+a^4
=[(x^2+5ax)+4a^2][(x^2+5ax)+6a^2]+a^4
=(x^2+5ax)^2+ 10(x^2+5ax)a^2 + 24a^2+a^4
=(x^2+5ax)^2+ 10(x^2+5ax)a^2 + 25a^2
=[(x^2+5ax)+5a^2]^2
=(x^2+5ax+5a^2)^2
=[(x-p)(x-q)]^2

其中p,q用求根公式,得:

p=-5a/2+sqrt(25a^2/4-5a^2)
=-5a/2+sqrt(5a^2/4)
=-5a/2+sqrt(5)a/2
=[-5+sqrt(5)]a/2

q=[-5-sqrt(5)]a/2