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BC
1
30 tháng 9 2015
A=x2y+xy2+xyz+xyz+y2z+yz2+x2z+xyz+xz2-xyz
A=(x2y+xy2+xyz+y2z)+(yz2+x2z+xyz+xz2)
A=y(x2+xy+xz+yz)+z(yz+x2+xy+xz)
A=(y+z)(x2+xy+xz+yz)
A=(y+z)[x(x+y)+z(x+y)]
A=(y+z)(x+y)(x+z)
10 tháng 7 2017
a) xy(x + y) + yz(z + y) + zx(z + x) + 3xyz
= [xy(x + y) + xyz] + [yz(z + y) + xyz] + [zx(z + x) + xyz]
= xy(x + y + z) + yz(x + y + z) + zx(x + y + z)
= (xy + yz + zx)(x + y + z)
b) Vô câu hỏi tương tự
26 tháng 7 2017
a) xy(x + y) + yz(z + y) + zx(z + x) + 3xyz
= [xy(x + y) + xyz] + [yz(z + y) + xyz] + [zx(z + x) + xyz]
= xy(x + y + z) + yz(x + y + z) + zx(x + y + z)
= (xy + yz + zx)(x + y + z)
b) tương tự
KY
16 tháng 9 2019
\(x\left(y^2-z^2\right)+y\left(z^2-x^2\right)+z\left(x^2-y^2\right)\)
\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2\)
\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2-xyz+xyz\)
\(=\left(yz^2-xz^2-xyz+x^2z\right)-\left(zy^2-xyz-xy^2+x^2y\right)\)
\(=z\left(yz-xz-xy+x^2\right)-y\left(zy-xz-xy+x^2\right)\)
\(=\left(z-y\right)\left(yz-xz-xy+x^2\right)\)
\(=\left(z-y\right)\left[y\left(z-x\right)-x\left(z-x\right)\right]\)
\(=\left(z-y\right)\left(y-x\right)\left(z-x\right)\)
CM
17 tháng 4 2019
Ta có
C = xyz – (xy + yz + zx) + x + y + z – 1
= (xyz – xy) – (yz – y) – (zx – x) + (z – 1)
= xy(z – 1) – y(z – 1) – x(z – 1) + (z – 1)
= (z – 1)(xy – y – x + 1)
= (z – 1).[y(x – 1) – (x – 1)]
= (z – 1)(y – 1)(x – 1)
Với x = 9; y = 10; z = 101 ta có
C = (101 – 1)(10 – 1)(9 – 1) = 100.9.8 = 7200
Đáp án cần chọn là: C
LT
2
12 tháng 8 2015
xyz + xz + yz + x + y + z + xy + 1
= ( xyz + xy ) + ( xz + yz ) + ( x + y) + ( z + 1 )
= xy ( z + 1 ) + z ( x + y ) + ( x+ y) + (z + 1 )
= ( xy + 1 )(z-1) + ( x+ y)(z + 1 )
= (z + 1 )(xy + x + y + 1 )
MT
12 tháng 8 2015
xyz + xz + yz + x + y + z + xy + 1
= ( xyz + xy ) + ( xz + yz ) + ( x + y) + ( z + 1 )
= xy ( z + 1 ) + z ( x + y ) + ( x+ y) + (z + 1 )
= ( xy + 1 )(z-1) + ( x+ y)(z + 1 )
= (z + 1 )(xy + x + y + 1 )
=(z + 1)[ x.(y+1)+(y+1)]
=(z+1)(y+1)(x+1)
CH
Cô Hoàng Huyền
Admin
VIP
26 tháng 9 2017
a) \(\left(x-y\right)^2+\left(y-z\right)^3+\left(z-x\right)^3\)
\(=\left(x-y\right)^2+\left(y-z+z-x\right)\left[\left(y-z\right)^2-\left(y-z\right)\left(z-x\right)+\left(z-x\right)^2\right]\)
\(=\left(x-y\right)^2+\left(y-x\right)\left(x^2+y^2+3z^2-3yz+xy-3xz\right)\)
\(=\left(x-y\right)\left(x-y-x^2-y^2-3z^2+3yz-xy+3xz\right)\)
Cô nghĩ phân tích đa thức này sẽ đẹp hơn:
\(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)
\(=\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]+\left(z-x\right)^3\)
\(=\left(x-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]+\left(z-x\right)^3\)
\(=\left(x-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2-\left(z-x\right)^2\right]\)
\(=\left(x-z\right)\left(3y^2-3xy+3zx-3xyz\right)\)
\(=3\left(x-y\right)\left(y-z\right)\left(z-x\right)\)
b) \(\left(x+y+z\right)\left(xy+yz+zx\right)-xyz\)
\(=\left(xy+yz+zx\right)\left(x+y+z\right)-xyz\)
\(=xy\left(x+y+z\right)+\left(yz+zx\right)\left(x+y+z\right)-xyz\)
\(=xy\left(x+y+z-z\right)+\left(yz+zx\right)\left(x+y+z\right)\)
\(=xy\left(x+y\right)+z\left(y+x\right)\left(x+y+z\right)\)
\(=\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]\)
\(=\left(x+y\right)\left(xy+zx+zy+z^2\right)\)
\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
6 tháng 7 2022
a) \left(x-y\right)^2+\left(y-z\right)^3+\left(z-x\right)^3(x−y)2+(y−z)3+(z−x)3
=\left(x-y\right)^2+\left(y-z+z-x\right)\left[\left(y-z\right)^2-\left(y-z\right)\left(z-x\right)+\left(z-x\right)^2\right]=(x−y)2+(y−z+z−x)[(y−z)2−(y−z)(z−x)+(z−x)2]
=\left(x-y\right)^2+\left(y-x\right)\left(x^2+y^2+3z^2-3yz+xy-3xz\right)=(x−y)2+(y−x)(x2+y2+3z2−3yz+xy−3xz)
=\left(x-y\right)\left(x-y-x^2-y^2-3z^2+3yz-xy+3xz\right)=(x−y)(x−y−x2−y2−3z2+3yz−xy+3xz
\left(x-y\right)^3+\left(y-z\right)^3+\left
=\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]+\left(z-x\right)^3
=\left(x-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]+\l
=\left(x-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2-\left(z-x\
=\left(x-z\right)\left(
=3\left(x-y\right)\lefb) \left(x+y+z\right)\left(xy+yz+zx\right)-xyzb)(x+y+z)(xy+yz+zx)−xyz
=\left(xy+yz+zx\right)\left(x+y+z\right)-xyz=(xy+yz+zx)(x+y+z)−xyz
=xy\left(x+y+z\right)+\left(yz+zx\right)\left(x+y+z\right)-xyz=xy(x+y+z)+(yz+zx)(x+y+z)−xyz
=xy\left(x+y+z-z\right)+\left(yz+zx\right)\left(x+y+z\right)=xy(x+y+z−z)+(yz+zx)(x+y+z)
=xy\left(x+y\right)+z\left(y+x\right)\left(x+y+z\right)=xy(x+y)+z(y+x)(x+y+z)
=\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]=(x+y)[xy+z(x+y+z)]
=\left(x+y\right)\left(xy+zx+zy+z^2\right)=(x+y)(xy+zx+zy+z2)
=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]=(x+y)[x(y+z)+z(y+z)]
=\left(x+y\right)\left(y+z\right)\left(z+x\right)=(x+y)(y+z)(z+x)
xy( x+ y) + yz(y+z) + xz(x+z) + 3xyz
= xy(x+y) + xyz + yz(y+z) + xyz + xz(x+z) + xyz
= zy(x+y+z) + yz(x + y + z) + xz ( x+y+z)
= ( x+ y +z )( xy + yz + zx)