(x² y - y² x) + (x² z - xyz) + (z² y - z² x) + (y² z - xyz) = (x-y)(xy+zx-z² -yz)=(x-y)(x-z)(y+z)=0

Giải giùm rồi đấy bạn

Giải giùm mik nha!

bạn nhiều câu hỏi quá

x²y - y²x+x²z - z²x +y²z +z²y - 2xyz = 0 

=> xy.(x - y) + xz. (x - z) + zy.(y + z) - xyz - xyz = 0 

=> [xy.(x - y) - xyz] + [xz.(x - z) - xyz] + zy,(y +z) = 0 

=> xy.(x - y - z) + xz.(x - z - y) + zy.(y +z) = 0

<=> (x-y-z). (y+z).x + zy.(y +z) = 0 

<=> (y +z). [x(x - y - z) + zy] = 0 

<=> y + z = 0 hoặc x(x - y - z) + zy = 0 

+) y + z = 0 => y;z đối nhau

+) x(x- y - z) + zy = 0 => x (x - y)  - z.(x - y) = 0  => (x - z)(x - y) = 0 => x = z hoặc x = y

Vậy ....

\(x^2y-xy^2+x^2z-xz^2+y^2z+yz^2=2xyz\)

\(\Leftrightarrow\left(x^2y-xy^2\right)+\left(x^2z-xyz\right)-\left(xz^2-yz^2\right)-\left(xyz-y^2z\right)=0\)

\(\Leftrightarrow xy\left(x-y\right)+xz\left(x-y\right)-z^2\left(x-y\right)-yz\left(x-y\right)=0\)

\(\Leftrightarrow\left(x-y\right)\left(xy+xz-z^2-yz\right)=0\)

\(\Leftrightarrow\left(x-y\right)\left[x\left(y+z\right)-z\left(y+z\right)\right]=0\)

\(\Leftrightarrow\left(x-y\right)\left(x-z\right)\left(y+z\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=y\\x=z\\y=-z\end{matrix}\right.\)\(\left(đpcm\right)\)

tu gia thiet =>(x²y-y²x)+(x²z-2xyz+y^2z)-(z²x-z²y)=0

                    <=>xy(x-y)+z(x-y)^2-z^2(x-y)=0

                     <=>(x-y)(xy-zx-zy-z^2)=0

        <=>..... ta dc dpcm

a: \(70a+84b-20ab-24b^2\)

\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)

\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)

\(=\left(5a+6b\right)\left(14-4b\right)\)

\(=2\left(7-2b\right)\left(5a+6b\right)\)

b: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2\right)+\left(y^2z+yz^2\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+2xyz+xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z+x\right)\)

\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z+x\right)\)

\(=\left(y+z\right)\cdot x\left(x+y+z\right)+yz\left(y+z+x\right)\)

\(=\left(y+z+x\right)\cdot\left(xy+xz+yz\right)\)

c: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2+2xyz\right)+\left(y^2z+yz^2\right)\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2xz\right)+yz\left(y+z\right)\)

\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)

\(=\left(y+z\right)\left(x^2+yz+xy+xz\right)\)

\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)

Bài này bạn phải chuyển 2xyz sang vế kia rồi nhóm hợp lí mới ra được

(x²y+z²y-2xyz)-(y²x-y²z)+(x²z-z²x)=0

y(x²+z²-2xz)-y²(x-z)+xz(x-z)=0

y(x-z)(x-z)-y²(x-z)+xz(x-z)=0

(x-z)(xy-yz-y²+xz)=0

(x-z)(x-y)(y+z)=0

Nên x-z=0 hoặc x-y=0 hoặc y+z=0

Do đó: x=z hoặc x=y hoặc y=-z

a) \(70a+84b-20ab-24b^2\)

\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)

\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)

\(=\left(5a+6b\right)\left(14-4b\right)\)

\(=2\left(5a+6b\right)\left(7-2b\right)\)

b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xyz+xz^2\right)+\left(xyz+y^2z+yz^2\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)

c) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

\(=\left(x^2y+xy^2\right)+\left(xz^2+yz^2\right)+\left(x^2z+2xyz+y^2z\right)\)

\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x^2+2xy+y^2\right)\)

\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x+y\right)^2\)

\(=\left(x+y\right)\left[xy+z^2+z\left(x+y\right)\right]\)

\(=\left(x+y\right)\left(xy+z^2+xz+yz\right)\)

\(=\left(x+y\right)\left[\left(xy+yz\right)+\left(xz+z^2\right)\right]\)

\(=\left(x+y\right)\left[y\left(x+z\right)+z\left(x+z\right)\right]\)

\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

a, 70a + 84b - 20ab - 24b²

 = 14.(5a + 6b) - 4b(5a + 6b)

= (5a + 6b).(14 - 4b) 

a, 70a + 84b - 20ab - 24b²

 = (70a + 84b) - (20ab + 24b²)

= 14.(5a + 6b) - 4b.(5a + 6b)

= (5a + 6b).(14 - 4b)