Phân tích đa thức thành nhân tử :
a) xy(x+y)+yz(y+z)+xz(x+z)+2xyz
b) 2bx-3ay-bby+ax
c) 5ab-3bx+ax+5y
K
Khách
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KY
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)
TA
28 tháng 7 2017
1 ) \(x^2-x-y^2-y=\left(x^2-y^2\right)+\left(-x-y\right)=\left(x+y\right)\left(x-y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
2 ) \(x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y+z\right)\left(x-y-z\right)\)
3 ) \(5x-5y+ax-ay=5.\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)
4 ) \(a^3-a^2x-ay+xy=a^2.\left(a-x\right)-y.\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)
5 ) \(xy.\left(x+y\right)+yz.\left(y+z\right)+xz.\left(x+z\right)+2xyz\)
\(=xy.\left(x+y\right)+y^2z+yz^2+x^2z+xz^2+xyz+xyz\)
\(=xy.\left(x+y\right)+\left(y^2z+xyz\right)+\left(yz^2+xz^2\right)+\left(x^2z+xyz\right)\)
\(=xy.\left(x+y\right)+yz.\left(x+y\right)+z^2.\left(x+y\right)+xz.\left(x+y\right)\)
\(=\left(x+y\right)\left(xy+yz+z^2+xz\right)=\left(x+y\right)\left[\left(xy+xz\right)+\left(yz+z^2\right)\right]\)
\(=\left(x+y\right)\left[x.\left(y+z\right)+z.\left(y+z\right)\right]=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
SM
4
D
13 tháng 8 2018
tao có \(xz\left(z-x\right)+yz\left(y+z\right)-xy\left(x+y\right)=xz\left(z-x\right)+yz\left(y+x+z-x\right)-xy\left(x+y\right)=xz\left(z-x\right)+yz\left(z-x\right)+yz\left(x+y\right)-xy\left(x+y\right)\)
\(\left(z-x\right)\left(xz+yz\right)+\left(x+y\right)\left(yz-xy\right)=\left(z-x\right)z\left(x+y\right)+\left(x+y\right)y\left(z-x\right)=\left(z-x\right)\left(x+y\right)\left(z+y\right)\)
nếu mình giải khó hiểu thì cho mình xin lỗi nhé
13 tháng 8 2018
\(xz\left(z-x\right)+yz\left(y+z\right)-xy+\left(x+y\right)\)
\(=xz^2-x^2z+yx\left(y+z\right)-xy\left(x+y\right)\)
\(=xz^2-x^2z+zy^2+z^2y-xy\left(x+y\right)\)
\(=xz^2-x^2z+zy^2+z^2y-x^2y-xy^2\)
P/s: ko chắc
chỗ nào k hiểu hỏi mình lại ớ
\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=xy\left(x+y\right)+xyz+xz\left(x+z\right)+xyz+yz\left(y+z\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\)
\(=x\left(y+z\right)\left(x+y+z\right)+yz\left(y+z\right)\)
\(=x\left(y+z\right)\left(x+y+z+yz\right)\)