化简:(1)(2x-y+z-2c+m)(m+y-2x-2c-z);(2)(a+3b)(a2-3ab+9b2)-(a-3b
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/09/20 17:26:46
化简:
(1)(2x-y+z-2c+m)(m+y-2x-2c-z);
(2)(a+3b)(a2-3ab+9b2)-(a-3b)(a2+3ab+9b2);
(3)(x+y)2(y+z-x)(z+x-y)+(x-y)2(x+y+z)(x+y-z).
(1)(2x-y+z-2c+m)(m+y-2x-2c-z);
(2)(a+3b)(a2-3ab+9b2)-(a-3b)(a2+3ab+9b2);
(3)(x+y)2(y+z-x)(z+x-y)+(x-y)2(x+y+z)(x+y-z).
(1)(2x-y+z-2c+m)(m+y-2x-2c-z),
=[(m-2c)+(2x-y+z)]•[(m-2c)-(2x-y+z)],
=(m-2c)2-(2x-y+z)2,
=m2-4cm+4c2-(4x2+y2+z2-4xy+4xz-2yz),
=m2-4cm+4c2-4x2-y2-z2+4xy-4xz+2yz;
(2)(a+3b)(a2-3ab+9b2)-(a-3b)(a2+3ab+9b2),
=(a3+27b3)-(a3-27b3),
=54b3;
(3)(x+y)2(y+z-x)(z+x-y)+(x-y)2(x+y+z)(x+y-z),
=(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],
=(x+y)2z2-(x-y)2z2,
=4xyz2.
=[(m-2c)+(2x-y+z)]•[(m-2c)-(2x-y+z)],
=(m-2c)2-(2x-y+z)2,
=m2-4cm+4c2-(4x2+y2+z2-4xy+4xz-2yz),
=m2-4cm+4c2-4x2-y2-z2+4xy-4xz+2yz;
(2)(a+3b)(a2-3ab+9b2)-(a-3b)(a2+3ab+9b2),
=(a3+27b3)-(a3-27b3),
=54b3;
(3)(x+y)2(y+z-x)(z+x-y)+(x-y)2(x+y+z)(x+y-z),
=(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],
=(x+y)2z2-(x-y)2z2,
=4xyz2.
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