6) \(9x^3y^2+3x^2y^2=3x^2y^2\left(3x+1\right)\)

7) \(x^3+2x^2+3x=x\left(x^2+2x+3\right)\)

8) \(6x^2y+4xy^2+2xy=2xy\left(3x+2y+1\right)\)

9) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=5x\left(x-2y\right)\left(x-3\right)\)

10) \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(3+5x\right)\)

6) 9x³y² + 3x²y² = 3x²y²( 3x + 1 )

7) x³ + 2x² + 3x = x( x² + 2x + 3 )

8) 6x²y + 4xy² + 2xy = 2xy( 3x + 2y + 1 )

9) 5x²( x - 2y ) - 15x( x - 2y ) = 5x( x - 2y )( x - 3 )

10 3( x - y ) - 5x( y - x ) = 3( x - y ) + 5x( x - y ) = ( x - y )( 3 + 5x )

a, \(9x^3y^2+3x^2y^2=3x^2y^2\left(3x+1\right)\)

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

c, \(6x^2y+4xy^2+2xy=2xy\left(3x+2y+1\right)\)

d, \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=\left(5x^2-15x\right)\left(x-2y\right)=5x\left(x-3\right)\left(x-2y\right)\)

e, \(3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)=\left(3+5x\right)\left(x-y\right)\)

16) 2x + 2y - x² - xy = ( 2x + 2y ) - ( x² + xy ) = 2( x + y ) - x( x + y ) = ( x + y )( 2 - x )

17) x² - 2x - 4y² - 4y = ( x² - 4y² ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2( x + 2y ) = ( x + 2y )( x - 2y - 2 )

18) x²y - x³ - 9y + 9x = ( x²y - x³ ) - ( 9y - 9x ) = x²( y - x ) - 9( y - x ) = ( y - x )( x² - 9 ) = ( y - x )( x - 3 )( x + 3 )

19) x²( x - 1 ) + 16( 1 - x ) = x²( x - 1 ) - 16( x - 1 ) = ( x - 1 )( x² - 16 ) = ( x - 1 )( x - 4 )( x + 4 )

20) 2x² + 3x - 2xy - 3y = ( 2x² - 2xy ) + ( 3x - 3y ) = 2x( x - y ) + 3( x - y ) = ( x - y )( 2x + 3 )

20, \(2x^2+3x-2xy-3y=2x\left(x-y\right)+3\left(x-y\right)=\left(2x+3\right)\left(x-y\right)\)

16, \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)

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

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

19, \(x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x^2-16\right)\left(x-1\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)

Bài 1: Phân tích đa thức thành nhân tử bằng phương pháp đặt nhân tử chung

16) 2x + 2y - x² - xy

   =  ( 2x - x² ) + ( 2y - xy )

   =   x ( 2 - x )  +  y ( 2 - x ) 

   =   ( 2 - x ) ( x + y )

17) x² - 2x - 4y² - 4y

    = ( x² - 4y² ) - ( 2x + 4y )

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

    = ( x + 2y ) ( x - 2y - 2 )

18) x²y - x³ - 9y +9x

    = ( 9x + x³ ) + ( x²y - 9y )

    =  x ( 9 + x² ) +  y ( x² - 9 ) 

    =   x ( 9 + x² ) - y ( 9 + x² )

    = ( 9 + x² ) ( x - y )

    = ( 3 - x ) ( 3 + x ) ( x - y )

19) x² ( x - 1) + 16 (1 - x )

 =   x² ( x - 1 ) - 16 ( x - 1 )

 = ( x - 1 ) ( x² - 16 )

 = ( x - 1 ) ( x - 4 ) ( x + 4 )

20) 2x² + 3x - 2xy - 3y

   =  2x² + 3x - ( 2xy + 3y )

   =   x ( 2x + 3 ) - y ( 2x + 3 )

   = ( 2x + 3 )  ( x - y )

b: \(x^2-6x+xy-6y\)

\(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

c: \(2x^2+2xy-x-y\)

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

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

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

1

a, 2x²+4x+2-2y² = 2(x²+2x+1-y²)= 2[(x+1)²-y² ] = 2(x-y+1)(x+y+1)

b, 2x - 2y - x² + 2xy - y²= 2(x -y) - (x² - 2xy + y²) = 2(x-y)-(x-y)²=(x-y)(2-x+y)

c, x²-y²-2y-1=x²-(y²+2y+1)=x²-(y+1)²=(x-y-1)(x+y+1)

d, x²-4x-2xy-4y+y²= x²-2xy+y²-4x-4y=(x-y)

2.

a, x²-3x+2=x²-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)

b, x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)

c, x²+6x-6=

e) Ta có: \(a^3-a^2-a+1\)

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

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

\(=\left(a-1\right)^2\cdot\left(a+1\right)\)

f) Ta có: \(x^3-2xy-x^2y+2y^2\)

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

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

a) \(\left(a^2+b^2\right)^2-4a^2b^2=\left(a^2+b^2+2ab\right)\left(a^2+b^2-2ab\right)=\left(a+b\right)^2.\left(a-b\right)^2\)

b) \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)

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

d) Đề sai ko ???

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

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

a, \(=\left(a^2+b^2-2ab\right)\left(a^2+b^2+2ab\right)=\left(\left(a-b\right)\left(a+b\right)\right)^2=\left(a^2-b^2\right)^2\)

\(b,=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)

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

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

\(e,=a^2\left(a-1\right)-\left(a-1\right)=\left(a-1\right)\left(a^2-1\right)\)

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

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

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

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

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

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

c) \(x^6-x^4+2x^3+2x^2=\left(x^6+2x^3+1\right)-\left(x^4-2x^2+1\right)\)

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

d) \(x^3+3x^2+3x+1-8y^3=\left(x+1\right)^3-8y^3=\left(x+1-2y\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)