若(3x+1)5=ax5+bx4+cx3+dx2+ex+f,求a-b+c-d+e-f的值.急用!

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若(3x+1)5=ax5+bx4+cx3+dx2+ex+f,求a-b+c-d+e-f的值.急用!

若(3x+1)5=ax5+bx4+cx3+dx2+ex+f,求a-b+c-d+e-f的值.急用!
若(3x+1)5=ax5+bx4+cx3+dx2+ex+f,求a-b+c-d+e-f的值.急用!

若(3x+1)5=ax5+bx4+cx3+dx2+ex+f,求a-b+c-d+e-f的值.急用!
3x+1)^5
=(3x)^5+5(3x)^4+10(3x)^3+10(3x)^2+5(3x)+1
=243x^5+405x^4+270x^3+90x^2+15x+1
=ax^5+bx^4+cx^3+dx^2+ex+f
对应同次项的系数是相等的,也就是
a=243,b=405,c=270,d=90,e=15,f=1
a-b+c-d+e-f=32

令x=-1
则(-3+1)^5=-a+b-c+d-e+f
两边乘-1
a-b+c-d+e-f=32

令X=-1,可得-32=-(a-b+c-d+e-f),所以a-b+c-d+e-f=32