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(x2+y2+z2)(x+y+z)2+(xy+yz+xz)
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1 tháng 11 2021
\(1,\\ a,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\\ b,=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\\ c,=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\\ d,=x\left(x-2y\right)+t\left(x-2y\right)=\left(x+t\right)\left(x-2y\right)\\ 2,\\ \Rightarrow x^2-4x+4-x^2+9=6\\ \Rightarrow-4x=-7\Rightarrow x=\dfrac{7}{4}\\ 3,\\ a,x^2+2x+2=\left(x+1\right)^2+1\ge1>0\\ b,-x^2+4x-5=-\left(x-2\right)^2-1\le-1< 0\)
CM
13 tháng 10 2017
x 2 y + x y 2 + x 2 z + x z 2 + y 2 z + y z 2 + 3xyz.
= ( x 2 y + x 2 z + xyz) + (x y 2 + y 2 z + xyz) + (x z 2 + y z 2 + xyz)
= x(xy + xz + yz) + y(xy + yz + xz) + z(xz + yz + xy)
= (x + y + z)(xy + xz + yz).
NC
14 tháng 12 2020
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+x^2z+xyz\right)+\left(xz^2+yz^2+xyz\right)+\left(xy^2+y^2z+xyz\right)\)
\(=x\left(xy+xz+yz\right)+z\left(xz+yz+xy\right)+y\left(xy+yz+xz\right)\)
\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)
KY
1
PT
1
HK
1
B1
14 tháng 8 2017
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
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xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
VD
4
25 tháng 7 2019
\(xy\left(x-y\right)+yz\left(y-z\right)+xz\left(z-x\right)\)
\(=xy\left(x-y\right)+yz\left[\left(y-x\right)-\left(z-x\right)\right]+xz\left(z-x\right)\)
\(=xy\left(x-y\right)-yz\left(x-y\right)-yz\left(z-x\right)+xz\left(z-x\right)\)
\(=\left(x-y\right)\left(xy-yz\right)-\left(z-x\right)\left(yz-xz\right)\)
\(=\left(x-y\right)\left(xy-yz\right)+\left(z-x\right)\left(xz-yz\right)\)
\(=\left(xy-yz\right)\left(x-y+z-x\right)\)
\(=\left(xy-yz\right)\left(-y+z\right)\)
28 tháng 7 2019
mơn bn nha ^^
nh sáng nay lên lp thầy chữa bài thì kq nó k như z, cả cách lm nx :v
kq là: ( z - y )( x - z)( y - x )
NT
0
LC
1
MT
4 tháng 9 2015
xy(x-y)+yz(y-z)+xz(x-z)
=y.[x.(x-y)+z.(y-z)]+xz(x-z)
=y.(x2-xy+zy-z2)+xz.(x-z)
=y.[(x2-z2)+(-xy+zy)]+xz.(x-z)
=y.[(x-z)(x+z)-y.(x-z)]+xz.(x-z)
=y.(x-z)(x+z-y)+xz.(x-z)
=(x-z)[y.(x+z-y)+xz]
=(x-z)(xy+yz-y2+xz)
VT
2
28 tháng 9 2016
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z2)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
28 tháng 9 2016
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)