搜搜考试网14 因式分解
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/06/25 07:59:23
14 因式分解
x^2-(m^2+n^2)x+mn(m^2-n^2)
=x^2-(m^2+n^2)x+m(m+n)·n(m-n)
=[x-m(m+n)][x-n(m-n)]
=(x-m^2-mn)(x-n^2+mn)
(ax-by)^3+(by-cz)^3-(ax-cz)^3
=(ax-by+by-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2]-(ax-cz)^3
=(ax-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2-(ax-cz)^2]
=(ax-cz){(ax-by)^2-(ax-by)(by-cz)+[(by-cz)+(ax-cz)][(by-cz)-(ax-cz)]}
=(ax-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-2cz+ax)(by-ax)]
=(ax-cz)(ax-by)(ax-by-by+cz-by+2cz-ax)
=3(ax-cz)(ax-by)(cz-by)
=x^2-(m^2+n^2)x+m(m+n)·n(m-n)
=[x-m(m+n)][x-n(m-n)]
=(x-m^2-mn)(x-n^2+mn)
(ax-by)^3+(by-cz)^3-(ax-cz)^3
=(ax-by+by-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2]-(ax-cz)^3
=(ax-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2-(ax-cz)^2]
=(ax-cz){(ax-by)^2-(ax-by)(by-cz)+[(by-cz)+(ax-cz)][(by-cz)-(ax-cz)]}
=(ax-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-2cz+ax)(by-ax)]
=(ax-cz)(ax-by)(ax-by-by+cz-by+2cz-ax)
=3(ax-cz)(ax-by)(cz-by)