若(3x+1)4=ax4+bx3+cx2+dx+e,则a-b+c-d+e=_.
问题描述:
若(3x+1)4=ax4+bx3+cx2+dx+e,则a-b+c-d+e=______.
答
∵(3x+1)4=(9x2+6x+1)2=81x4+108x3+54x2+12x+1,
(3x+1)4=ax4+bx3+cx2+dx+e,
∴81x4+108x3+54x2+12x+1=ax4+bx3+cx2+dx+e,
∴a=81,b=108,c=54,d=12,e=1,
∴a-b+c-d+e=81-108+54-12+1=16.
故答案是16.