Question

7年级数学一题

求（2x^6-3x^5+4x^4-7x^3+2x-5)(3x^5-x^3+2x^2-5)的展开式中x^8与x^4的系数

帮帮忙很急

Answer 1

首先要想:如何得到X^8和X^4
X^4可以由X*X^3得
也可以由X^2*X^2得
也可以由1*X^4得

同理
X^8的系数是2*2+3-3*7=-14
X^4的系数是-5*4-2*1=-22

Answer 2

-1，-22

Answer 3

x^8的系数 2*2+3*1-7*3= -14

x^4的系数 -4*5-2*1=-22

Answer 4

4x^8+3x^8-21x^8=-14x^8
x^8的系数=-14

-20x^4-2x^4=-22x^4
x^4的系数=-22

Answer 5

2*2+(-3)*(-1)+(-7)*3=-14
4*(-5)+2*(-1)=-22

Answer 6

（2x^6-3x^5+4x^4-7x^3+2x-5)(3x^5-x^3+2x^2-5)
=6x^11-2x^9+4x^8-10x^6-9x^10+3x^8-6x^7+15x^5+12x^9-4x^7+8x^6-20x^4-21x^8+7x^6-14x^5+35x^3+6x^6-2x^4+4x^3-10x-15x^5+5x^3-10x^2+25
=6x^11-9x^10+12x^9-2x^9-21x^8+4x^8+3x^8-6x^7-4x^7+7x^6-10x^6+6x^6+8x^6+15x^5-15x^5-14x^5-20x^4-2x^4+35x^3+4x^3+5x^3-10x^2-10x+25
= 6x^11-9x^10+10x^9-14x^8-10x^7+4x^6-14x^5-22x^4+44x^3-10x^2-10x+25
所以x^8与x^4的系数分别为-14和22