因式分解：x^2+4y^2+9z^2-4xy-12yz+6xz

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/27 16:33:13

因式分解：x^2+4y^2+9z^2-4xy-12yz+6xz
(1)x^2+4y^2+9z^2-4xy-12yz+6xz
(2)x^3+6x^2+11x+6
(3)x^3+3x^2+3x-26
(4)x^3+4x^2-13x-24
(5)6x^4+5x^3+3x^2-3x-2
(6)2x^3-ax^2-5a^2x-2a^3

(1)x^2+4y^2+9z^2-4xy-12yz+6xz
=x^2-4xy+4y^2+6xz-12yz+9z^2
=(x-2y)^2+6z(x-2y)+9z^2
=(x-2y+3z)^2
(2)x^3+6x^2+11x+6
=x^3+x^2+5x^2+5x+6x+6
=x^2(x+1)+5x(x+1)+6(x+1)
=(x^2+5x+6)(x+1)
=(x+2)(x+3)(x+1)
(3)x^3+3x^2+3x-26
= x^3+3x^2+3x+1-27
=(x+1)^3-3^3
=(x+1-3)((x+1)^2+3(x+1)+3^2)
=(x-2)(x^2+5x+13)
(4)x^3+4x^2-13x-24
=(x^3-27)+(4x^2-13x+3)
=(x-3)(x^2+3x+9)+(4x-1)(x-3)
=(x-3)(x^2+3x+9+4x-1)
=(x-3)(x^2+7x+8)
(5)6x^4+5x^3+3x^2-3x-2
=6x^4+5x^3+x^2+2x^2-3x-2
=x^2(2x+1)(3x+1)+(2x+1)(x-2)
=(2x+1)(3x^3+x^2+x-2)
=(2x+1)(3x^3-3+x^2+x+1)
=(2x+1)[3(x-1)(x^2+x+1)+x^2+x+1]
=(2x+1)(3x-2)(x^2+x+1)
(6)2x^3-ax^2-5a^2x-2a^3
=2x^3-ax^2-(2a^2x+3a^2x)-2a^3
=(2x^3-2a^2x)-(ax^2+3a^2x+2a^3)
=2x(x+a)(x-a)-a(x+a)(x+2a)
=(x+a)[2x(x-a)-a(x+2a)]
=(x+a)[2x^2-3ax-2a^2]
=(x+a)(x-2a)(2x+a)

(2X+Z-Y)/(X^2-XY+XZ-YZ)-(Y-Z)/(X^2-XY-XZ+YZ) 如果3y=x+2y,那么x *x+9*y*y+4*z*z-6xy-12yz+4xz的值是多少? 若x/2=1/y=z/3,且xy+xz+yz=99,求4x^2-2xz+3yz-9y^2的值. x^2+y^2+xy=25/4,x^2+z^2+xz=169/4,y^2+z^2+yz=36,求xy+xz+yz 如果3y=x+2z,那么x^2+9y^2+4z^2-6xy-12yz+4xz= 若x/3=y=z/4,且xy+xz+yz=76,求2x*x+12y*y+9z*z的值因式分解x^2-xy+xz-yz 求(2X+Z-Y)/(X^2-XY+XZ-YZ)-(2X+Y+Z)/(X^2+XY+XZ+YZ) 因式分解x^2+y^2+z^2+2xy+2yz+2xz-2x-2y-2z+1 化简(2x-y-z/x^2-xy-xz+yz)+(2y-x-z/y^2-xy-yz+xz)+(2x-x-y/z^2-xz 若X/3=Y/1=Z/4,且XY+XZ+YZ=76,求2X^2+12Y^2+9Z^2的值若x/3=y/1=z/4,且xy+xz+yz=76,求2x²+12y²+9z²的值