`Answer:`

`m-3xyz+5x^2-7xy+9=6x^2+xyz+2xy+3-y^2`

`<=>m=(6x^2+xyz+2xy+3-y^2)+(3xyz-5x^2+7xy-9)`

`<=>(xyz+3xyz)+(6x^2-5x^2)+(2xy+7xy)-y^2+(3-9)`

`<=>m=4xyz+x^2+9xy-y^2-6`

\(3xyz^2+\left(-\frac{4}{8}\right)xyz^5\cdot\frac{1}{3}xyz\)

\(=3xyz^2-\frac{1}{2}xyz\cdot\frac{1}{3}xyz\)

\(=3xyz-\frac{1}{6}x^2y^2z^2\)

\(xyz\left(3-\frac{1}{6}xyz\right)\)

b) \(3xyz^5\cdot\left(-\frac{1}{7}\right)xyz\cdot\frac{-1}{8}xyz^4\)

\(=\left[3\cdot\left(-\frac{1}{7}\right)\cdot\left(-\frac{1}{8}\right)\right]\left(x\cdot x\cdot x\right)\left(y\cdot y\cdot y\right)\left(z^5\cdot z\cdot z^4\right)\)

\(=\frac{3}{56}x^3y^3z^{10}\)

a, \(3xyz^2+\left(\frac{-4}{8}xyz^5\right)\cdot\frac{1}{3}xyz=3xyz^2+\left[\left(\frac{-4}{8}\right)\cdot\frac{1}{3}\right]xyz^5xyz\)\(=3xyz^2-\frac{1}{2}x^2y^2z^6\)

b, \(3xyz^5\cdot\left(\frac{-1}{7}xyz^2\right)\cdot\frac{-1}{8}xyz^4=\left[3\cdot\left(\frac{-1}{7}\right)\cdot\left(\frac{-1}{8}\right)\right]xyz^5xyz^2xyz^4=\frac{3}{56}x^3y^3z^{11}\)

đặt 3 xy làm chung nha bn ...

~ hok tốt ~

chung 3xy nhek

\(3x^3y-6x^2y-3xy^3-6xy^2z-3xyz^2+3xy\)

\(=3xy\left(x^2-2x-y^2-2yz-x^2+1\right)\)

\(=3xy\left(\left(x^2-2x+1\right)-\left(y^2+2yz+z^2\right)\right)\)

\(=3xy\left(\left(x-1\right)^2-\left(y-z\right)^2\right)\)

\(=3xy\left(x-1+y-z\right)\left(x-1-y+z\right)\)

\(3x^3y-6x^2y-3xy^3-6xy^2z-3xyz^2+3xy\)

\(=3xy\left(x^2-2x-y^2-2yz-z^2+1\right)\)

\(=3xy\left[\left(x-1\right)^2-\left(y+z\right)^2\right]\)

\(=3xy\left(x-1-y-z\right)\left(x-1+y+z\right)\)

Ta có:

M = 3xyz - 3x² + 5xy - 1

N = 5x² + xyz - 5xy + 3 - y

M + N = 3xyz - 3x² + 5xy - 1 + 5x² + xyz - 5xy + 3 - y

= -3x² + 5x² + 3xyz + xyz + 5xy - 5xy - y - 1 + 3

= 2x² + 4xyz - y +2.

M - N = (3xyz - 3x² + 5xy - 1) - (5x² + xyz - 5xy + 3 - y)

= 3xyz - 3x² + 5xy - 1 - 5x² - xyz + 5xy - 3 + y

= -3x² - 5x² + 3xyz - xyz + 5xy + 5xy + y - 1 - 3

= -8x² + 2xyz + 10xy + y - 4.

N - M = (5x² + xyz - 5xy + 3 - y) - (3xyz - 3x² + 5xy - 1)

= 5x² + xyz - 5xy + 3 - y - 3xyz + 3x² - 5xy + 1

= 5x² + 3x² + xyz - 3xyz - 5xy - 5xy - y + 3 + 1

= 8x² - 2xyz - 10xy - y + 4.

M = 3xyz - 3x² + 5xy - 1

N = 5x² + xyz - 5xy + 3 - y

M + N = 3xyz - 3x² + 5xy - 1 + 5x² + xyz - 5xy + 3 - y

= -3x² + 5x² + 3xyz + xyz + 5xy - 5xy - y - 1 + 3

= 2x² + 4xyz - y +2.

M - N = (3xyz - 3x² + 5xy - 1) - (5x² + xyz - 5xy + 3 - y)

= 3xyz - 3x² + 5xy - 1 - 5x² - xyz + 5xy - 3 + y

= -3x² - 5x² + 3xyz - xyz + 5xy + 5xy + y - 1 - 3

= -8x² + 2xyz + 10xy + y - 4.

N - M = (5x² + xyz - 5xy + 3 - y) - (3xyz - 3x² + 5xy - 1)

= 5x² + xyz - 5xy + 3 - y - 3xyz + 3x² - 5xy + 1

= 5x² + 3x² + xyz - 3xyz - 5xy - 5xy - y + 3 + 1

= 8x² - 2xyz - 10xy - y + 4.

M = 3xyz - 3x2 + 5xy - 1

N = 5x2 + xyz - 5xy + 3 - y

M + N = 3xyz - 3x2 + 5xy - 1 + 5x2 + xyz - 5xy + 3 - y

= -3x2 + 5x2 + 3xyz + xyz + 5xy - 5xy - y - 1 + 3

= 2x2 + 4xyz - y +2.

M - N = (3xyz - 3x2 + 5xy - 1) - (5x2 + xyz - 5xy + 3 - y)

= 3xyz - 3x2 + 5xy - 1 - 5x2 - xyz + 5xy - 3 + y

= -3x² - 5x² + 3xyz - xyz + 5xy + 5xy + y - 1 - 3

= -8x² + 2xyz + 10xy + y - 4.

N - M = (5x ²+ xyz - 5xy + 3 - y) - (3xyz - 3x² + 5xy - 1)

= 5x² + xyz - 5xy + 3 - y - 3xyz + 3x² - 5xy + 1

= ( 5x² + 3x² ) + xyz - 3xyz - 5xy - 5xy - y + 3 + 1

= 8x² - 2xyz - 10xy - y + 4.

M+N

\(=3xyz-3x^2+5xy-1+5x^2+xyz-5xy+3\)

\(=2x^2+4xyz+2\)

M-N

\(=3xyz-3x^2+5xy-1-5x^2-xyz+5xy-3\)

\(=-8x^2+2xyz+10xy-4\)

ta có : ( 15x³ -8x³-17x³) - (3x⁵+3x⁵)+(6x² - 6x²)-2x+11 =  -10x³ -2x + 11

đề bài là gì vậy bạn

 \(M + N = (3xyz – 3x^2 + 5xy – 1) + (5x^2 + xyz – 5xy + 3 – y)\)

      \(= 3xyz – 3x^2 + 5xy – 1 + 5x^2 + xyz – 5xy + 3 – y\)

      \(= (3xyz + xyz)+( –3x^2 + 5x^2) + (5xy – 5xy) – y + ( – 1+3)\)

      \(= 4xyz + 2x^2 – y + 2\)

 \(M – N = (3xyz – 3x^2 + 5xy – 1) – (5x^2 + xyz – 5xy + 3 – y)\)

      \(= 3xyz – 3x^2 + 5xy – 1 – 5x^2 – xyz + 5xy – 3 + y\)

      \(= (– 3x^2 – 5x^2) + (3xyz – xyz) + (5xy + 5xy) + y +(– 1 – 3)\)

      \(= –8x^2 + 2xyz + 10xy + y – 4.\)

\(N – M = (5x^2 + xyz – 5xy + 3 – y) – (3xyz – 3x^2 + 5xy – 1)\)

      \(= 5x^2 + xyz – 5xy + 3 – y – 3xyz + 3x^2 – 5xy +1\)

      \(= (5x^2 + 3x^2)+ (xyz – 3xyz)+( – 5xy – 5xy) + (3 + 1 )– y\)

      \(= 8x^2 – 2xyz – 10xy – y + 4.\)

M+N=(3xyz-3x³+5xy-1)+(5x²+xyz-5xy+3-y)

        =3xyz-3x³+5xy-1+5x²+xyz-5xy+3-y

        =(3xyz+xyz)+(-3x³)+(5xy-5xy)+(-1+3)+5x²-y

        =   4xyz+(-3x³)+2+5x²-y

M-N=(3xyz-3x³+5xy-1)-(5x²+xyz-5xy+3-y)

       =3xyz-3x³+5xy-1-5x²-xyz+5xy-3+y

       =(3xyz-xyz)+(-3x³)+(5xy+5xy)+(-1-3)-5x²+y

       =   2xyz+(-3x³)+10xy+(-4)-5x²+y