①如果要使关于X,Y的多项式mx^3+2nxy^2+2x^3-xy^2+y不含3次项,则m+2n=()
题目写错了w应该是x
由于不含3次项,
故x^3项的系数为0 ==> m+2=0 ==>m=-2
xy^2项的系数为0 ==> 2n-1=0 ==>n=1/2
m+2n=()=-2+2*(1/2)=-1
②化简4（a-b）^2+2(b-a)^3-3(a-b)^3-3(b-a)^2
=4（a-b）^2-2(a-b)^3-3(a-b)^3-3(a-b)^2
=（a-b）^2-5(a-b)^3
=(1-5a+5b)（a-b）^2
③当X+1的绝对值=0时,求多项式：-3x^(n+1) -x^n +6x^(n+1) +3x^n -x^n+1的值
-3x^(n+1) -x^n +6x^(n+1) +3x^n -x^n+1
=3x^(n+1)+x^n +1
X+1的绝对值=0
故x=-1 代入原式得
3*((-1)^(n+1)) +(-1)^n +1
当n为奇数时
=3-1+1
=3
当n为偶数时
=-3+1+1
=-1
④设A=-x^2 +4x^3 +5,B=ax^3 +5x -b,若A+B中不含X的三次项和常数项,试求a,b的值.
A+B
=-x^2 +4x^3 +5+ax^3 +5x -b
=(a+4)x^3-x^2 +5x+5-b
不含X的三次项
故a+4=0==>a=-4
不含常数项
故5-b=0==>b=5