(x+i)(x+2)(x+3)(x+4)+1求化简过程

2025-03-01 12:55:27
推荐回答(2个)
回答1:

=[(x+1)(x+4)][(x+2)(xc+3)]+1
=[(x²+5x)+4][(x²+5x)+6]+1
=(x²+5x)²+10(x²+5x)+24+1
=(x²+5x)²+10(x²+5x)+25
=(x²+5x+5)²

回答2:

(x+1)(x+2)(x+3)(x+4)+1
=[(x+1)(x+4)][(x+2)(x+3)]+1
=(x^2+5x+4)(x^2+5x+6)+1
令x^2+5x=t
=(t+4)(t+6)+1
=t^2+10t+25
=(t+5)^2
=(x^2+5x+5)^2