$\displaystyle \begin{array}{{>{\displaystyle}l}} a) 3x^{3} y^{2} -6x^{2} y^{3} +9x^{2} y^{2}\\ =3x^{2} y^{2}( x-2y+3) \ \\ b) 12x^{2} y-18xy^{2} -30y^{2}\\ =6y\left( 2x^{2} -3xy-5y\right)\\ =6y\left( 2x^{2} -5xy+2xy-5y\right)\\ =6y[ 2x( x-5y) +y( x-5y)]\\ =6y( 2x+y)( x-5y) \ \\ c) \ 4x( 2y-z) +7y( z-2y)\\ =( 2y-z)( 4x-7y) \ \\ d) 27x^{2}( y-1) -9x^{3}( 1-y)\\ =\left( 27x^{2} +9x^{3}\right)( y-1)\\ =9x^{2}( x+3)( y-1) \ \\ e)\left( x^{2} +1\right)^{2} -6\left( x^{2} +1\right) +9\ \\ =\left( x^{2} +1\right)^{2} -2.3\left( x^{2} +1\right) +9\\ =\left( x^{2} +1-3\right)^{2} =\left( x^{2} -2\right)^{2} \ \\ f) \ 9( x+5)^{2} -( x+7)^{2}\\ =( 3x+15-x-7)( 3x+15+x+7)\\ =( 2x-8)( 4x+22)\\ =4( x-4)( 2x+11) \ \\ g) 49( y-4)^{2} -9( y+2)^{2}\\ =( 7y-28+3y+6)( 7y-28-2y-6)\\ =( 10y-22)( 5y-34)\\ =2( 5y-22)( 5y-34) \ \\ h) -( x+2) +3\left( x^{2} -4\right)\\ =-( x+2) +3( x-2)( x+2)\\ =( x+2)( 3x-6-1) =( x+2)( 3x-7) \ \\ \end{array}$

`@Mon`

`@\text{ Bài 1:}`

`a)3x^3y^2-6x^2y^3+9x^2y^2`

`=3x^2y^2.(x-2y+3)`

`b)12x^2y-18xy^2-30y^2`

`=6y.(2x-3xy-5y)`

`c)4x.(2y-z)+7y(z-2y)`

`=4x.(2y-z)-7y(2y-z)`

`=(2y-z)(4x-7y)`

`d)27x^2(y-1)-9x^3(1-y)`

`=27x^2.(y-1)+9x^3(y-1)`

`=9x^2.(y-1)(3+x)`

`e)(x^2+1)^2-6.(x^2+1)+9`

`=(x^2+1)^2-3(x^2+1)-3(x^2+1)+3^2`

`=(x^2+1).(x^2+1-3)`

`(x^2-2)^2`

`f)9(x+5)^2-(x+7)^2`

`=[3(x+5)]^2-(x+7)^2`

`=(3x+15-x-7)(3x+15+x+7)`

`=(2x+8)(4x+2x)`

`=4.(x+4)(2x+11)`

`g)49(y-4)^2-9(y+z)^2`

`=[7(y-4)]^2-[3(y+2)]^2`

`=(7y-28-3y-6)(7y-28+3y+6)`

`=(4y-34)(10y-22)`

`=4(2y-17)(5y-11)`

`h)-(x+2)+3(x^2-4)`

`=-(x+2)+3(x-2)(x+2)`

`=(x+2)(-1+3x-6)`

`=(x+2)(3x-7)`

`@\text{ Bài 2:}`

`a)5(x+3_-2x(x+3)=0`

`<=>5(x+3)(5-2x)=0`

`<=>` \(\left[ \begin{array}{l}x+3=0\\5-2x=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=-3\\x=\dfrac{5}{2}\end{array} \right.\) 

`b)6x(x^2-2)-(2-x^2)=0`

`<=>6x(x^2-2)+(x^2-2)=0`

`<=>(6x+1)(x^2-2)=0`

`<=>` \(\left[ \begin{array}{l}6x+1=0\\x^2-2=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}6x=-1\\x^2=2\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=\dfrac{-1}{6}\\\pm\sqrt{2}\end{array} \right.\) 

`c)(x+1)^2-(x+1)(x-2)=0`

`<=>(x+1)[(x+1)-(x-2)]=0`

`<=>(x+1)=0`

`<=>x=-1`

`d)4x(x-2017)-x+2017=0`

`<=>4x(x-2017)-(x-2017)=0`

`<=>(4x-1)(x-2017)=0`

`<=>`\(\left[ \begin{array}{l}4x-1=0\\x-2017=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{4}\\x=2017\end{array} \right.\) 

`e)(x+4)^2-16=0`

`<=>(x+4)^2=16`

`<=>(x+4)^2=(+-4)^2`

`<=>`\(\left[ \begin{array}{l}x+4=4\\x+4=-4\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0\\x=-8\end{array} \right.\) 

`f)12x-x^2-36=0`

`<=>-(x^2-12x+35)=0`

`<=>-(x-6)^2=0`

`<=>(x-6)^2=0`

`<=>x-6=0`

`<=>x=6`

`f)x(x-2012)-2013x+2012.2013=0`

`<=>x(x-2012)-2013(x-2012)=0`

`<=>(x-2012)(x-2013)=0`

`<=>`\(\left[ \begin{array}{l}x-2012=0\\x-2013=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=2012\\x=2013\end{array} \right.\)

`g)(x-1)^3+1+3x(x-4)=0`

`<=>x^3-3x^2+3x-1+1+3x^2-12x=0`

`<=>x^3-9x=0`

`<=>x(x^2-9)=0`

`<=>`\(\left[ \begin{array}{l}x=0\\x^2-9=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0\\x^2=9\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=0\\x=\pm3\end{array} \right.\)

`h)4x^2-25-(2x-5)(2x+7)=0`

`<=>(2x)^2-5^2-(2x-5)(2x+7)=0`

`<=>(2x-5)(2x+5)-(2x-5)(2x+7)=0`

`<=>(2x-5)[(2x+5)-(2x+7)]=0`

`<=>2x-5=0`

`<=>2x=5`

`<=>x=\frac{5}{2}`

`i_x^3+27+(x+3)(x-9)=0`

`<=>(x+3)(x^2+3x+9)+(x+3)(x-9)=0`

`<=>(x+3)(x^2+4x)=0`

`<=>`\(\left[ \begin{array}{l}x+3=0\\x^2+4x=0\end{array} \right.\) 

`<=>x=-3; x=0; x=-4`