phan tich da thuc thanh nhan tu
1+x+y+z+xy+yz+zx+xyz
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PN
10 tháng 1 2016
\(\left(x+y+z\right)\left(xy+yz+xz\right)-xyz=xy\left(x+y+z\right)-xyz+\left(yz+xz\right)\left(x+y+z\right)\)
\(=xy\left(x+y+z-z\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=xy\left(x+y\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]\)
\(=\left(x+y\right)\left(xy+xz+yz+z^2\right)\)
\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
NT
1
23 tháng 12 2019
Ta có : \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+xz\left(x+z\right)\)
\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+z\right)\)
\(=y\left(x+y+z\right)\left(x+z\right)+xz\left(x+z\right)\)
\(=\left(x+z\right)\left(xy+y^2+yz+xz\right)\)
\(=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)
LS
0
28 tháng 7 2017
\(yz\left(y+z\right)+xz\left(z-x\right)-xy\left(x+y\right)\)
\(=-[xy(x+y)-yz(y+z)-zx(z-x)]\)
\(=-(y.[x(x+y)-z(y+z)]-zx(z-x))\)
\(=-[y.(x^2+xy-zy-z^2)-zx(z-x)]\)
\(=-[y.(x^2-z^2+xy-zy)-zx(z-x)]\)
\(=-(y.[(x+z)(x-z)+y.(x-z)]-zx(z-x))\)
\(=-[y.(x-z)(x+z+y)+zx(x-z)]\)
\(=[(x-z)[y(x+z+y)+zx]]\)
\(=-(x-z)(yx+yz+y2+zx)\)
\(=-(x-z)(yx+zx+yz+y2)\)
\(=-[(x-z)[x.(y+z)+y.(y+z)]]\)
\(=-(x-z)(y+z)(x+y)\)
LS
0
9 tháng 7 2017
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
HG
1
LH
0
