a) `x^4+2x^3-4x-4`

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

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

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

b) `x^3-4x^2+12x-27`

`=(x^3-27)-(4x^2-12x)`

`=(x-3)(x^2+3x+9)-4x(x-3)`

`=(x-3)(x^2+3x+9-4x)`

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

c) `xy-4y-5x+20`

`=y(x-4)-5(x-4)`

`=(y-5)(x-4)`

a) Ta có: \(x^4+2x^3-4x-4\)

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

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

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

b) Ta có: \(x^3-4x^2+12x-27\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\cdot\left(x-3\right)\)

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

c) Ta có: \(xy-4y-5x+20\)

\(=y\left(x-4\right)-5\left(x-4\right)\)

\(=\left(x-4\right)\left(y-5\right)\)

1) \(4x^2-7x-2=4x^2-8x+x-2=\left(4x^2-8x\right)+\left(x-2\right)\)

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

2) \(4x^2+5x-6=4x^2+8x-3x-6=\left(4x^2+8x\right)-\left(3x+6\right)\)

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

3) \(5x^2-18x-8=5x^2-20x+2x-8=\left(5x^2-20x\right)+\left(2x-8\right)\)

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

4) \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

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

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

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

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

\(=xy\left(x+y\right)+\left(zx-zy\right)\left(x+y\right)-z^2\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+xz-yz-z^2\right)=\left(x+y\right).\left[x\left(y+z\right)-z\left(y+z\right)\right]\)

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

1) 4x² - 7x - 2 = 4x² - 8x + x - 2 = 4x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 4x + 1 )

2) 4x² + 5x - 6 = 4x² - 8x + 3x - 6 = 4x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 4x + 3 )

3) 5x² - 18x - 8 = 5x² - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )

4) xy( x + y ) - yz( y + z ) + xz( x - z )

= x²y + xy² - y²z - yz² + xz( x - z )

= ( x²y - yz² ) + ( xy² - y²z ) + xz( x - z )

= y( x² - z² ) + y²( x - z ) + xz( x - z )

= y( x - z )( x + z ) + y²( x - z ) + xz( x - z )

= ( x - z )[ y( x + z ) + y² + xz ]

= ( x - z )( xy + yz + y² + xz )

= ( x - z )[ ( xy + y² ) + ( xz + yz ) ]

= ( x - z )[ y( x + y ) + z( x + y ) ]

= ( x - z )( x + y )( y + z )

5) xy( x + y ) + yz + xz( x + z ) + 2xyz ( đề có thiếu không vậy .-. )

\(4x^2-7x-2=\left(4x^2-8x\right)+\left(x-2\right)=4x\left(x-2\right)+\left(x-2\right)=\left(4x-1\right)\left(x-2\right)\)

\(=4x^2+8x-3x-6=4x\left(x+2\right)-3\left(x+2\right)=\left(4x-3\right)\left(x+2\right)\)

\(=5x^2-18x-8=5x^2-20x+2x-8=5x\left(x-4\right)+2\left(x-4\right)=\left(5x+2\right)\left(x-4\right)\)

\(5=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)

1, \(x^2\left(x-3\right)-4x+12=x^2\left(x-3\right)-4\left(x-3\right)\)

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

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

3, \(2x-4+5x^2-10x=2\left(x-2\right)+5x\left(x-2\right)=\left(2+5x\right)\left(x-2\right)\)

4, sửa đề : 

 \(6x^2-12x-7x+14=6x\left(x-2\right)-7\left(x-2\right)=\left(6x-7\right)\left(x-2\right)\)

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

a) x²(x-3)-4x+12

=x²(x-3)-4(x-3)

=(x-3)(x²-4)

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

b) 2a(x+y)-x-y

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

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

c) 2x-4+5x²-10x

=2(x-2)+5x(x-2)

=(x-2)(2+5x)

d) 5x²-12x-7x+14

=5x²-19x+14

e) xy-y²-3x+3y

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

=(x-y)(y-3)

#H

Trả lời:

1, x² ( x - 3 ) - 4x + 12 = x² ( x - 3 ) - 4 ( x - 3 ) = ( x - 3 )( x² - 4 ) = ( x - 3 )( x - 2 )( x + 2 )

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

3, 2x - 4 + 5x² - 10x = ( 2x - 4 ) + ( 5x² - 10x ) = 2 ( x - 2 ) + 5x ( x - 2 ) = ( x - 2 )( 2 + 5x )

4, Sửa đề: 6x² - 12x - 7x + 14 = ( 6x² - 12x ) - ( 7x - 14 ) = 6x ( x - 2 ) - 7 ( x - 2 ) = ( x - 2 )( 6x - 7 )

5, xy - y² - 3x + 3y = ( xy - y² ) - ( 3x - 3y ) = y ( x - y ) - 3 ( x - y ) = ( x + y )( y - 3 )

1: =(x+y-3x)(x+y+3x)

=(-2x+y)(4x+y)

2: =(3x-1-4)(3x-1+4)

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

=3(x+1)(3x-5)

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

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

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

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

4: =(2x+1+x-1)(2x+1-x+1)

=3x(x+2)

5: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(2x^2+2)*4x

=8x(x^2+1)

6: =(5x-5y)^2-(4x+4y)^2

=(5x-5y-4x-4y)(5x-5y+4x+4y)

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

7: =(x^2+xy+y^2+xy)(x^2+xy-y^2-xy)

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

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

8: =(x^2+4y^2-20-4xy+16)(x^2+4y^2-20+4xy-16)

=[(x-2y)^2-4][(x+2y)^2-36]

=(x-2y-2)(x-2y+2)(x+2y-6)(x+2y+6)

Ta có : 5x(x - 2y) + 2(2y - x)²

= 5x(x - 2y) + 2(x - 2y)² (vì (2y - x)² = (x - 2y)² )

= (x - 2y)[5x + 2(x - 2y)]

= (x - 2y)(5x + 2x - 4y)

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

b) 7x(y - 4)² - (4 - y)³ 

= 7x(y - 4)² - (4 - y)²(4 - y)

= 7x(y - 4)² - (y - 4)²(4 - y)

= (y - 4)²(7x - 4 + y)

c) (4x - 8)(x² + 6) - (4x - 8)(x + 7) + 9(8 - 4x)

= (4x - 8)(x² + 6) - (4x - 8)(x + 7) - 9(4x - 8)

= (4x - 8)(x² + 6 - x - 7 - 9)

= 2(x - 4)(x² - x - 10)

a) = (x + 3)² - y² = (x + 3 - y)(x + 3 + y)

b) = x²(x - 3) -4(x - 3) = (x - 3)(x² - 4) = (x - 3)(x - 2)(x + 2)

c) = 3x(x - y) - 5(x - y) = (x - y)(3x - y)

d) Nhầm đề. tui sửa lại x³ + y³ + 2x² - 2xy + 2y²

= x³ + y³ + 2(x² - xy + y²) = (x + y)(x² - xy + y²) + 2(x² - xy + y²) = (x² - xy + y²)(x + y + 2)

e) = x⁴ - x³ - x³ + x² - x² + x + x - 1 = x³(x - 1) - x²(x - 1) - x(x - 1) + x - 1 = (x - 1)(x³ - x² - x + 1) = (x - 1)(x - 1)(x² - 1) = (x - 1)³(x + 1)

f) = x³ - 3x² - x² + 3x + 9x - 27 = x²(x - 3) - x(x - 3) + 9(x - 3) = (x-3)(x² - x + 9)

g) chắc là 3xyz 

= x²y + xy² + y²z + yz² + x²z + xz² + 3xyz = x²y + xy² + xyz + y²z + yz² + xyz + x²z + xz² + xyz = (x + y + z)(xy + yz + xz)

h) = 2³ -(3x)³ = (2 - 3x)(4 + 6x + 9x²)

i) = (x + y - x + y)(x + y + x - y) = 2y*2x = 4xy

k) = (x³ - y³)(x³ + y³) = (x - y)(x² + xy +y2)(x + y)(x² - xy +y2).

1) \(x^2-6x+3\)

\(=x^2-6x+9-6\)

\(=\left(x-3\right)^2-6\)

\(=\left(x-3+\sqrt{6}\right)\left(x-3-\sqrt{6}\right)\)

2) \(2m^2+10m+8\)

\(=2m^2+2m+8m+8\)

\(=2m\left(m+1\right)+8\left(m+1\right)\)

\(=\left(2m+8\right)\left(m+1\right)\)

\(=2\left(m+4\right)\left(m+1\right)\)

3) \(9x^2+6x-8\)

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

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

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

4) \(x^3-5x^2-14x\)

\(=x\left(x^2-5x-14\right)\)

\(=x\left(x^2-2x+7x-14\right)\)

\(=x\left[x\left(x-2\right)+7\left(x-2\right)\right]\)

\(=x\left(x+7\right)\left(x-2\right)\)

1) x^2-6x+3

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

=(x-3)^2-6

=(x-3-căn 6)(x-3+căn 6)

2) =2(m^2+5m+4)

=2(m+1)(m+4)

3) =9x^2+6x+1-9

=(3x+1)^-9

=(3x-2)(3x+4)

4, x^3-5x^2-14x

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

5, a^4+4a^2-5

=a^4+4a^2+4-9

=(a^2+2)^-9

=(a^2-1)(a^2+5)

6, x^3-7x-6

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

5) \(a^4+4a^2-5\)

\(=a^4+5a^2-a^2-5\)

\(=a^2\left(a^2+5\right)-\left(a^2+5\right)\)

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

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

6) \(x^3-7x-6\)

\(=x^3-x-6x-6\)

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

\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)

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

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

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

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