三道代数计算题⑴6x2-5xy-6y2-2xz-23yz-20z2⑵x3+6x2+12x+9⑶x2y-y2z+z2x最后
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/03 03:38:26
三道代数计算题
⑴6x2-5xy-6y2-2xz-23yz-20z2
⑵x3+6x2+12x+9
⑶x2y-y2z+z2x
最后一道题应该是
x2y-y2z+z2x-x2z+y2x+z2y-2xyz
⑴6x2-5xy-6y2-2xz-23yz-20z2
⑵x3+6x2+12x+9
⑶x2y-y2z+z2x
最后一道题应该是
x2y-y2z+z2x-x2z+y2x+z2y-2xyz
6x²-5xy-6y²-2xz-23yz-20z²
=6x^2-(5y+2z)x-6y^2-23yz-20z^2
=6[x^2-(5/6y+1/3z)x+(3/2y+2z)(-2/3y-5/3)z
=6(x-3/2y+2z)(x+2/3y+5/3z)
=(2x-3y+4z)(3x+2y+5z)
x3+6x2+12x+9
=X(X+3)2+3(X+3)
=(x+3)(x2+3x+3)
x2y-y2z+z2x-x2z+y2x+z2y-2xyz
=(x2y+xy2-xyz)-(x2z+xyz-z2x)-y2z+yz2
=xy(x+y-z)-xz(x+y-z)-yz(y-z)
=x(x+y-z)(y-z)-yz(y-z)
=(y-z)[(x2+xy)-(xz+yz)]
=(y-z)(x+y)(x-z)
=6x^2-(5y+2z)x-6y^2-23yz-20z^2
=6[x^2-(5/6y+1/3z)x+(3/2y+2z)(-2/3y-5/3)z
=6(x-3/2y+2z)(x+2/3y+5/3z)
=(2x-3y+4z)(3x+2y+5z)
x3+6x2+12x+9
=X(X+3)2+3(X+3)
=(x+3)(x2+3x+3)
x2y-y2z+z2x-x2z+y2x+z2y-2xyz
=(x2y+xy2-xyz)-(x2z+xyz-z2x)-y2z+yz2
=xy(x+y-z)-xz(x+y-z)-yz(y-z)
=x(x+y-z)(y-z)-yz(y-z)
=(y-z)[(x2+xy)-(xz+yz)]
=(y-z)(x+y)(x-z)
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