x 4 - 2 x 3 - 2 x 2 - 2 x - 3 =   ( x 4   −   1 )   −   ( 2 x 3   +   2 x 2 )   −   ( 2 x   +   2 ) =   ( x 2   +   1   ) ( x 2   −   1 )   −   2 x 2 ( x   +   1 )   − 2 ( x   +   1 ) =   ( x 2   +   1 ) ( x   −   1 ) ( x   +   1 )   −   2 x 2 ( x   +   1 )   − 2 ( x   +   1 ) =   ( x   +   1 ) ( x 2   +   1 ) ( x   −   1 )   −   2 x 2   –   2 =   ( x   +   1 ) (   x 2   +   1 ) ( x   −   1 )   −   2 ( x 2   +   1 ) =   ( x   +   1 ) (   x 2   +   1 ) ( x   –   1   −   2 ) =   ( x   +   1 ) (   x 2   +   1 ) ( x   −   3 )

x^4 - 2x^3 - 2x^2 - 2x - 3 

= x^4 - 1 - 2x^3 - 2x^2 - 2x -2 

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

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

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

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

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

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

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

\(x^4+4\)

= \(\left(x^2+2\right)^2-4x^2\)

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

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

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

c) \(x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2-x+9\right)\)

d) \(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a-1\right)\left(a+1\right)+2\left(a+1\right)\right]=a^2\left(a+1\right)\left(a^3-a^2+2\right)=a^2\left(a+1\right)\left[a^3+a^2-2a^2+2\right]=a^2\left(a+1\right)\left[a^2\left(a+1\right)-2\left(a-1\right)\left(a+1\right)\right]=a^2\left(a+1\right)^2\left(a^2-2a+2\right)\)

a) Ta có: \(x^2-2x-4y^2-4y\)

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

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

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

b) Ta có: \(x^3+2x^2+2x+1\)

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

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

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

d) Ta có: \(a^6-a^4+2a^3+2a^2\)

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

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

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

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

c) Ta có: \(x^3-4x^2+12x-27\)

\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)

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

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

Đa thức này không phân tích được thành nhân tử bạn nhé. 

`x^4+x^2 y^2+y^4`

`=x^4+2x^2 y^2 +y^4-x^2 y^2`

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

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

e) Ta có: \(x^4-2x^3+2x-1\)

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

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

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

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

h) Ta có: \(3x^2-3y^2-2\left(x-y\right)^2\)

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

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

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

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

a) Ta có: \(x^2-y^2-2x-2y\)

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

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

b) Ta có: \(x^2\left(x+2y\right)-x-2y\)

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

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

c) Ta có: \(x^3-4x^2-9x+36\)

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

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

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

d) Ta có: \(x^4+2x^3+2x-1\)

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

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

${}^{}-2{}^{}+2x-1$

$={}^{}-{}^{}-{}^{}+{}^{}-{}^{}+x+x-1$

$={}^{}\left(x-1\right)-{}^{}\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)$

$=\left(x-1\right)\left({}^{}-{}^{}-x+1\right)$
$=\left(x-1\right)[$

\(x^4+2x^3+2x^2+2x+1\\ =\left(x^4+x^3\right)+\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)\\ =x^3\left(x+1\right)+x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\\ =\left(x^3+x^2+x+1\right)\left(x+1\right)\\ =\left[\left(x^3+x^2\right)+\left(x+1\right)\right]\left(x+1\right)\\ =\left[x^2\left(x+1\right)+\left(x+1\right)\right]\left(x+1\right)\\ =\left(x^2+1\right)\left(x+1\right)^2\)

\(x^4+2x^3+2x^2+2x+1\)

\(=x^4+x^3+x^3+x^2+x^2+2x+1\)

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

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

\(=\left(x+1\right)^2\cdot\left(x^2+1\right)\)