a: \(=\left(-\dfrac{6}{2}\right)\cdot\dfrac{x^3}{x}\cdot\dfrac{y^2}{y^2}=-3x^2\)

b: \(=\left(-\dfrac{1}{4}:\dfrac{1}{2}\right)\cdot\dfrac{x^4}{x^3}\cdot\dfrac{y^3}{y^2}=-\dfrac{1}{2}xy\)

c: \(=\dfrac{8}{4}\cdot\dfrac{x^4}{x^3}\cdot\dfrac{y^5}{y^4}=2xy\)

\(a,-6x^3y^2:2xy^2=-3x^2\)

\(b,-\dfrac{1}{4}x^4y^3:\dfrac{1}{2}x^3y^2=-\dfrac{1}{2}xy\)

\(c,8x^4y^5:4x^3y^4=2xy\)

#Urushi

1) \(x^3\left(\dfrac{-5}{4}x^2y\right)\left(\dfrac{2}{5}x^3y^4\right)\)

\(=\dfrac{-1}{2}x^8y^5\)

Vậy: Bậc là 14, phần hệ số là \(\dfrac{-1}{2}\)

2) \(5xyz.4x^3y^2\left(-2x^5y\right)\)

\(=-40x^9y^4z\)

Vậy: Bậc là 15, phần hệ số là \(-40\)

3) \(4x^3y\left(-x^2y^5\right)\left(2xy\right)\)

\(=-8x^6y^7\)

Vậy: Bậc là 14, phần hệ số là \(-8\)

1) \(4x^5y^2-8x^4y^2+4x^3y^2\)

\(=4x^3y^2\left(x^2-2x+1\right)\)

\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=4x^3y^2\left(x-1\right)^2\)

2) \(5x^4y^2-10x^3y^2+5x^2y^2\)

\(=5x^2y^2\left(x^2-2x+1\right)\)

\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=5x^2y^2\left(x-1\right)^2\)

3) \(12x^2-12xy+3y^2\)

\(=3\left(4x^2-4xy+y^2\right)\)

\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

4) \(8x^3-8x^2y+2xy^2\)

\(=2x\left(4x^2-4xy+y^2\right)\)

\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=2x\left(2x-y\right)^2\)

5) \(20x^4y^2-20x^3y^3+5x^2y^4\)

\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)

\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=5x^2y^2\left(2x-y\right)^2\)

1: 4x^5y^2-8x^4y^2+4x^3y^2

=4x^3y^2(x^2-2x+1)

=4x^3y^2(x-1)^2

2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)

3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)

4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)

5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)

\(a,\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-y=5\\2x+y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\ b,\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\23y=46\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)

\(c,\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\ d,\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

\(e,\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

a. \(\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}10x=20\\6x-2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

b. \(\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23y=46\\5x+2y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=1\end{matrix}\right.\)

c. \(\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)

d. \(\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\4x+3y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

e. \(\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\4x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

a) \(\begin{cases} 3x -y=5\\ 4x +2y=10 \end{cases} \)

    \(\begin{cases} 12x - 4y= 20\\ 12x +6y= 30 \end{cases} \)

    \(\begin{cases} -10y=-10\\ 3x-y=5 \end{cases} \)

    \(\begin{cases} y=1\\ 3x-1=5 \end{cases} \)

    \(\begin{cases} y=1\\ 3x=6 \end{cases} \)

    \(\begin{cases} y=1\\ x=2 \end{cases} \)

Hpt có nghiệm duy nhất: {1;2}

b)\(\begin{cases} 5x +2y=9\\ x+5y=11 \end{cases} \)

  \(\begin{cases} 5x+2y=9\\ 5x+25y=55 \end{cases} \)

  \(\begin{cases} -23y=-46\\ x+5y=11 \end{cases} \)

  \(\begin{cases} y=2\\ x+ 5*2=11 \end{cases} \)

  \(\begin{cases} y=2\\ x+10=11 \end{cases} \)

Hpt có nghiệm duy nhất:{1;2}

c)\(\begin{cases} 3x+y=10\\ 4x-3y=9 \end{cases} \)

  \(\begin{cases} 12x+4y=40\\ 12x-9y=27 \end{cases} \)

 \(\begin{cases} 13y=13\\ 3x+y=10 \end{cases} \)

 \(\begin{cases} y=1\\ 3x+1=10 \end{cases} \)

 \(\begin{cases} y=1\\ 3x=9 \end{cases} \)

hpt có nghiệm duy nhất:{1;3}

d)\(\begin{cases} 4x+3y=22\\ 5x+3y=26 \end{cases} \)

  \(\begin{cases} 20x+15y=110\\ 20x+12y=104 \end{cases} \)

 \(\begin{cases} 3y=6\\ 4x+3y=22 \end{cases} \)

 \(\begin{cases} y=2\\ 4x+3*2=22 \end{cases} \)

 \(\begin{cases} y=2\\ 4x+6=22 \end{cases} \)

hệ phương trình có nghiệm duy nhất:{2;4}

e)\(\begin{cases} 4x-3y=5\\ 5x+3y=13 \end{cases} \)

  \(\begin{cases} 20x-15y=25\\ 20x+12y=52 \end{cases} \)

 \(\begin{cases} -27y=-27\\ 4x-3y=5 \end{cases} \)

  \(\begin{cases} y=1\\ 4x-3*1=5 \end{cases} \)

   \(\begin{cases} y=1\\ 4x-3=5 \end{cases} \)

Hệ phương trình có nghiệm duy nhất là:{1;2}

\(c,\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\ d,\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\\ e,\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

c: \(\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x+4y=40\\12x-9y=27\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}13y=13\\3x+y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=3\end{matrix}\right.\)

d: \(\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x=-4\\4x+3y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{22-4x}{3}=\dfrac{22-4\cdot4}{3}=2\end{matrix}\right.\)

c. \(\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)

d. \(\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\4x+3y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

e. \(\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\4x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

\(a,\dfrac{2}{3}xy^2.\dfrac{2}{3}xy=\dfrac{4}{9}x^2y^3\)

\(b,-\dfrac{1}{2}x^2y.2xy^2=-x^3y^3\)

\(c,8xy^3.2x^3y^2=16x^4y^5\)

\(d,-\dfrac{1}{4}x^2y^3.2x^3y^2=-\dfrac{1}{2}x^5y^5\)

\(e,4x^2y^4.\dfrac{1}{2}x^2y^3=2x^4y^7\)

\(f,-8xy.\dfrac{1}{4}x^2y=-2x^3y^2\)

\(Ayumu\)