(2x-y+z-2c+m)(m+y-2x-2c-z)(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 11:10:42
(2x-y+z-2c+m)(m+y-2x-2c-z)(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)

(2x-y+z-2c+m)(m+y-2x-2c-z)(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)
(2x-y+z-2c+m)(m+y-2x-2c-z)
(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)
(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)

(2x-y+z-2c+m)(m+y-2x-2c-z)(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)
(2x-y+z-2c+m)(m+y-2x-2c-z)=m^2-4x^2-y^2+4c^2-z^2+4xy-4xz+2yz-4cm
(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)
=(a^3+27b^3)-(a^3-27b^3)
=54b^3;
设a=x+y,b=x-y,a+b=2x,a-b=2y
(x+Y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)(x+y-z)
=a^2(z-b)(z+b)+b^2(a+z)(a-z)
=a^2(z^2-b^2)+b^2(a^2-z^2)
=a^2z^2-a^2b^2+a^2b^2-b^2z^2
=a^2z^2-b^2z^2
=z^2(a^2-b^2)
=z^2(a+b)(a-b)
=z^2(2x*2y)
=4xyz^2