x⁴+4 = (x²)²+2² = x⁴ + 2.x².2 + 4 – 4x²

= (x² + 2)² – (2x)² = (x²-2x+2)(x²+2x+2)

Ta có: \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

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

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

x⁴ + x²y² +y⁴                   

= (x²)² +  x²y² + (y²)²          

= (x²)² +  x²y² + (y²)²  + x²y² - x²y²       

= (x²)² +  2 x²y² + (y²)²  - x²y²      

= (x² + y²)²- (xy)²                  

=(x² + y² + xy)(x² + y² - xy)

x4 + 4

= (x2)2 + 22

= x4 + 2.x2.2 + 4 – 4x2

(Thêm bớt 2.x2.2 để có HĐT (1))

= (x2 + 2)2 – (2x)2

(Xuất hiện HĐT (3))

= (x2 + 2 – 2x)(x2 + 2 + 2x)

x4 – 2x2

(Có x2 là nhân tử chung)

= x2(x2 – 2)

x 4 - 5 x 2 + 4 = x 4 - 4 x 2 - x 2 + 4 = x 4 - 4 x 2 - x 2 - 4 = x 2 x 2 - 4 - x 2 - 4 = x 2 - 4 x 2 - 1 = x + 2 x - 2 x + 1 x - 1

Sửa đề: x^4+4y^4

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

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

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

x⁴ - 2x³ + 2x - 1

= (x⁴ - 1) - (2x³ - 2x)

= (x² - 1)(x² + 1) - 2x(x² - 1)

= (x² - 1)(x² + 1 - 2x)

= (x - 1)(x + 1)(x² - 2x + 1)

= (x - 1)(x + 1)(x - 1)²

= (x - 1)³(x + 1)

Ta có:

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

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

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

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

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

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

x 8   +   x 4   +   1     =   x 8   +   2 x 4     +   1   –   x 4       =   ( x 8   +   2 x 4     +   1 )   –   x 4       =   [ ( x 4 ) 2   +   2 . x 4   . 1   +   12 ]   –   x 4     =   ( x 4   +   1 ) 2   –   ( x 2 ) 2     =   ( x 4   +   1   –   x 2 ) ( x 4   +   1   +   x 2 )     =   ( x 4   –   x 2   +   1 ) ( x 4   +   2 x 2   –   x 2   +   1 )     =   ( x 4   –   x 2   +   1 ) [ ( ( x 2 ) 2   +   2 . 1 . x 2   +   1 )   –   x 2 ] =   ( x 4   –   x 2   +   1 ) [ ( x 2   +   1 ) 2   –   x 2 ]     =   ( x 4   –   x 2   +   1 ) ( x 2   +   1   –   x ) ( x 2   +   1   +   x )     =   ( x 4   –   x 2   +   1 ) ( x 2   –   x   +   1 ) ( x 2   +   x   +   1 )

Đáp án cần chọn là: C