(x+y)4(x-y)4

显示全部楼层 · 2008-1-31 17:18:18

(1) (x+y)^4(x-y)^4=[(x+y)(x-y)]^4=(x^2-y^2)^4=[(x^2-y^2)^2]^2= (x^4-2x^2y^2+y^4)^2=x^8+4x^4y^4+y^8-4x^6y^2+2x^4y^4-4x^2y^6;(2) (a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)=(a^3+27b^3)-(a^3-27b^3)=54b^3； (3)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)*(x+y-z)=(x+y)^2*[z^2-(x-y)^2]+(x-y)^2*[(x+y)^2-z^2]=(x+y)^2z^2-(x+y)^2(x-y)^2+(x-y)^2(x+y)^2-(x-y)^2z^2=(xz+yz)^2-(xz-yz)^2=x^2z^2+2xyz^2+y^2z^2-x^2z^2+2xyz^2-y^2z^2=4xyz^2; 4．因为(x^2-2x+3)*(2x+7)+7x-19=f(x)=2x^3+3x^2-x+2，f(x)/(x2-2x+3)所得的商式为2x+7.

千问 · 2008-1-31 17:18:18

(1) =[（x+y)(x-y)]4 =[x2-y2]4 =(x4-2x2y2+y4)(x4-2x2y2+y4) =x8+4x4y4+y8-4x6y2-4x2y6+2x4y4 =x8+y8+6x4y4-4x6y2-4x2y6 (2) =a3-3a2b+9ab2+3a2b-9ab2+27b3 -(a3+3a2b+9ab2-3a2b-9ab2-27b3) =-6a2b+6a2b+54b3 =54b3 (3) =(x+y)2[z-(x-y)][z+(x-y)]+(x-y)2[(x+y)+z][(x+y)-z] =(x+y)2[z2-(x-y)2]+(x-y)2[(x+y)2-z2] =z2(x+y)2-(x+y)2(x-y)2+(x-y)2(x+y)2-z2(x-y)2 =0 (4) 2x3+3x2-x+2 =2x(x2-2x+3)+7x2-7x+2 =2x(x2-2x+3)+7(x2-2x+3)+7x-19 商式为2x+7,余式为7x-19好象是这样，我从我的习题里抄的，应该对的把。

千问 · 2008-1-31 17:18:18

1计算(x+y)4(x-y)4
=16x2-16y2
2是平方2简化(a+3b)(a2-3ab=9b2)-(a-3b)(a2+3ab+9b2)
=a3+(3b)3-a3+(3b)3
=54b3
是根据立方展开公式3是立方3原试=(x+y)2(x-y)2-z2-(x-y)2(x+y)2+z2
=0
此题关键是将x+y看成整体与Z形成平方差公式4 根据经典除法的出商试为2X+7
余试为 7X-19

千问 · 2008-1-31 17:18:18

(1)=[（x+y)(x-y)]4=[x2-y2]4=(x4-2x2y2+y4)(x4-2x2y2+y4)=x8+4x4y4+y8-4x6y2-4x2y6+2x4y4=x8+y8+6x4y4-4x6y2-4x2y6(2)=a3-3a2b+9ab2+3a2b-9ab2+27b3-(a3+3a2b+9ab2-3a2b-9ab2-27b3)=-6a2b+6a2b+54b3=54b3(3)=(x+y)2[z-(x-y)][z+(x-y)]+(x-y)2[(x+y)+z][(x+y)-z]=(x+y)2[z2-(x-y)2]+(x-y)2[(x+y)2-z2]=z2(x+y)2-(x+y)2(x-y)2+(x-y)2(x+y)2-z2(x-y)2=0(4)2x3+3x2-x+2=2x(x2-2x+3)+7x2-7x+2=2x(x2-2x+3)+7(x2-2x+3)+7x-19商式为2x+7,余式为7x-19(1)=(x^2-y^2)^4=x^8-4x^6y^2+6x^4y^4-4x^2y^6+y^8(2)=54b^3(3)=4xy*z^2(4)商式2x+7,余式7x-19