问题
填空题
若(x-3)4=ax4+bx3+cx2+dx+e,则b+c+d+e=______.
答案
∵(x-3)4=(x2-6x+9)2=x4-12x3+54x2-108x+81,
∴x4-12x3+54x2-108x+81=ax4+bx3+cx2+dx+e,
∴a=1,b=-12,c=54,d=-108,e=81,
∴b+c+d+e=-12+54-108+81=15.
若(x-3)4=ax4+bx3+cx2+dx+e,则b+c+d+e=______.
∵(x-3)4=(x2-6x+9)2=x4-12x3+54x2-108x+81,
∴x4-12x3+54x2-108x+81=ax4+bx3+cx2+dx+e,
∴a=1,b=-12,c=54,d=-108,e=81,
∴b+c+d+e=-12+54-108+81=15.