phân tích các đa thức sau thành nhân tử
a) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
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26 tháng 8 2018
a) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)
\(=\left(x+y+z\right)\left(xy+xz\right)+yz\left(y+z\right)\)
\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)
b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z+x\right)\)
\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)
P/s: Sai sót xin bỏ qua.
BC
2
20 tháng 10 2018
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)
H
13 tháng 12 2018
\(2xyz+x^2y+xy^2+x^2z+xz^2+y^2z+yz^2\)
\(=x^2\left(y+z\right)+yz\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y^2+z^2+2yz\right)\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)
\(=\left(y+z\right)\left(x^2+yz\right)+xy+xz\)
\(=\left(y+z\right)\left[x\left(x+2\right)+y\left(x+2\right)\right]\)
\(=\left(y+z\right)\left(x+y\right)\left(x+2\right)\)
H
13 tháng 12 2018
\(b,x^2\left(y-z\right)+y^2\left(z-y\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)+y^2z-y^2x+z^2x-z^2y\)
\(=x^2\left(y-z\right)+yz\left(y-z\right)-x\left(y^2-z^2\right)\)
\(=\left(y-z\right)\left[x^2+yz-x\left(y+z\right)\right]\)
\(=\left(y-z\right)\left[x\left(x-y\right)-z\left(x-y\right)\right]\)
\(=\left(y-z\right)\left[\left(x-z\right)\left(x-y\right)\right]\)
A
0
SE
1
19 tháng 8 2016
=xy ( x + y ) + z ( x^2 + 2xy + y^2 ) = xy ( x + y ) + z ( x + y ) ^ 2 = ( x + y ) ( xy + xz + yz )
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz.\)
\(=x^2.\left(y+z\right)+yz.\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)
\(=\left(y+z\right).\left(x^2+yz\right)+x\left(y^{^2}+z^2+2yz\right)\)
\(=\left(y+z\right).\left[x.\left(x+2\right)+y.\left(x+2\right)\right]\)
\(=\left(y+z\right).\left(x+z\right).\left(x+y\right)\)