x³-8y³-z³-6xyz

题目

x³-8y³-z³-6xyz
因式分解
还有：a²+b²+c²-2bc+2ca-2ab
(x+1)^4+(x^2-1)^2+(x_1)^4

答案

x^3+y^3+z^3-3xyz
= (x+y)(x^2+y^2-xy)+z^3-3xyz
= (x+y)[(x+y)^2-3xy]+z^3-3xyz
= (x+y)^3-3xy(x+y)+z^3-3xyz
= (x+y)^3+z^3-3xy(x+y)-3xyz
= (x+y+z)[(x+y)^2+z^2-z(x+y)]-[3xy(x+y)+3xyz]
= (x+y+z)(x^2+y^2+2xy+z^2-xz-yz)-3xy(x+y+z)
= (x+y+z)(x^2+y^2+z^2-xy-xz-yz)
把上面的y换成-2y,z换成-z
得
x³-8y³-z³-6xyz
=(x-2y-z)(x^2+4y^2+z^2+2xy+xz-2yz)