初一乘法公式

题目

初一乘法公式
1.求证:(x+y-2z)^3+(y+z-2x)^3+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)
2.在括号里填上适当的数或式,使等式成立
(1)x^2-1/2x+( )=(x-1/4)^2 (2)(a+b)^2+( )=(a-b)^2
(3)(1/2x-4)[1/4x^2+( )+16]=( )^3-( )^3
3.解方程.(5x+7)(5x-7)+(x+3)^2=10x^2-(4x+1)(-4x-1)+48
4.已知:(-4x+3y)(-3y-4x)减去多项式M的差为-36y^2+5xy,求M
5.已知：a+b+c=0,a^3+b^3+c^3=0求证a^19+b^19+c^19+0

答案

1.求证:(x+y-2z)^3+(y+z-2x)^3+(y+z-2x)=3(x+y-2z)(y+z-2x)(z+x-2y)令a=x+y-2z,b=y+z-2x,c=y+z-2x则a+b+c=0a^3+b^3+c^3-3abc=a^3+3a^2b+3ab^2+b^3+c^3-3a^2b-3ab^2-3abc =(a+b)^3+c^3-3ab(a+b+c) =(a+b+c)[(a+b)^2-(...