a) \(3xy-6xy^2=3xy\left(1-2y\right)\)

b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)

c) \(x^3-x^2+2\)

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

e) \(x^3+4x^2+4x=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)

f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)

g) \(6x^2-12x=6x\left(x-2\right)\)

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

i) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)

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

l) \(x^3-7x^2+9x+3x^2-21x+27=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)

a) = (x - 2)² - y²

= (x - 2 - y)(x + 2 + y)

b) = (x^2 + 6x + 9) - (2y)^2

= (x + 3)² - (2y)²

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

c) = (x - 3y)² - 6²

= (x - 3y - 6)(x - 3y + 6)

\(x^3-x^2-x+1\)

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

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

\(a.=x^3+3x^2y+3x^2y+9xy^2+3xy^2+9y^3\)

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

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

\(b.=9x^3+3x^2y+9x^2y+3xy^2+3xy^2+y^3\)

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

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

x^2+6xy+9y^2-3x-9y+2

=( x^2+6xy+9y^2)-3(x+3y)+9/4 -1/4

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

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

=(x+3y+3/2+1/2)(x+3y+3/2-1/2)=(x+3y+2)(x+3y+1)

a, \(6x^3y^2.\left(2-x\right)+9x^2y^2\left(x-2\right)\)
\(=6x^3y^2.\left(2-x\right)-9x^2y^2\left(2-x\right)\)
\(=y^2.\left(2-x\right)\left(6x^3-9x^2\right)\)
\(=3x^2y^2.\left(2-x\right)\left(2x-3\right)\)

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

a) \(3\left(x-y\right)^2+9y\left(y-x\right)^2\)

\(=3\left(x-y\right)^2+9y\left(x-y\right)^2\)

\(=\left(x-y\right)^2\left(3-9y\right)\)

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

b) \(3\left(x-y\right)^2+9y\left(y-x\right)\)

\(=3\left(y-x\right)^2+9y\left(y-x\right)\)

\(=\left(y-x\right)\left[3\left(y-x\right)+9y\right]\)

\(=3\left(y-x\right)\left(y-x+3y\right)\)

\(=3\left(y-x\right)\left(4y-x\right)\)

a: =3(x-y)^2+9y(x-y)^2

=(x-y)^2(3+9y)

=(x-y)^2*3*(y+3)

b: =3(x-y)^2-9y(x-y)

=3(x-y)(x-y-9y)

=3(x-y)(x-10y)

a) A = (x + 1)(y - 2) - (2 - y)²

= -[(x + 1)(2 - y) + (2 - y)²]

= -[(x + 1 - 2 + y)(2 - y)]

= -[(x - 1 + y)(2 - y)]

= (x - 1 + y)(y - 2)

Bài 2:

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

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

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

\(A=\left(y-2\right)\left(x-y+3\right)\)

b) \(B=x^2-6xy+9y^2+4x-12y\)

\(B=\left[x^2-2\cdot x\cdot3y+\left(3y\right)^2\right]+4\left(x-3y\right)\)

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

\(B=\left(x-3y\right)\left(x-3y+4\right)\)

Bài 3:

a) \(3\left(x-2\right)\left(x+3\right)-x\left(3x+1\right)=2\)

\(\left(3x^2+3x-18\right)-\left(3x^2+x\right)-2=0\)

\(3x^2+3x-18-3x^2-x-2=0\)

\(2x-20=0\)

\(x=10\)

b) \(6x^2+13x+5=0\)

\(6x^2+10x+3x+5=0\)

\(2x\left(3x+5\right)+\left(3x+5\right)=0\)

\(\left(3x+5\right)\left(2x+1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}3x+5=0\\2x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{-5}{3}\\x=\frac{-1}{2}\end{cases}}}\)

a) 3x² - 7x + 4

= 3x² - 3x - 4x + 4

= 3x( x - 1 ) - 4( x - 1 )

= ( x - 1 )( 3x - 4 )

b) x² - 6xy + 9y² = ( x - 3y )²

c) x² - 8x - 9

= x² - 9x + x - 9

= x( x - 9 ) + ( x - 9 )

= ( x - 9 )( x + 1 )

a) 3x² - 7x + 4

= 3x² - 4x - 3x + 4

= (3x² - 4x) - (3x - 4)

= x.(3x - 4) - (3x - 4)

= (3x - 4).(x - 1)

b) x² - 6xy + 9y²

= x² - 2.x.3y + (3y)²

= (x - 3y)²

c) x² - 8x - 9

= x² - 9x + x - 9

= (x² - 9x) + (x - 9)

= x.(x - 9) + (x - 9)

= (x - 9).(x + 1)