\(x^4+4\)

= \(\left(x^2+2\right)^2-4x^2\)

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

`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)`

x⁴ - 2x³-2x² -2x -3

=(x⁴+x³)-(3x³+3x²)+(x²+x)-(3x+3)

=x³(x+1)-3x²(x+1)+x(x+1)-3(x+1)

= (x³-3x²+x-3)(x+1)

= ((x³-3x²)+(x-3))(x+1)

= (x²(x-3)+(x-3))(x+1)

=(x²+1)(x-3)(x+1)

4x²-y²+4x+1

=(4x²+4x+1)-y²

=(2x+1)²-y²

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

bài này tớ cũng ko chắc:

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

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

\(4x^2-4x+1=\left(2x\right)^2-2.2x.1+1^2=\left(2x-1\right)^2\\ ---\\ 4x^2-4x-3\\ =4x^2-4x+1-4\\ =\left(2x-1\right)^2-2^2=\left(2x-1-2\right)\left(2x-1+2\right)\\ =\left(2x-3\right)\left(2x+1\right)\)

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

=(2x-1)^2

2: =4x^2-6x+2x-3

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

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

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

C1:        \(4x^2-4x+1=\left(2x-1\right)^2\)       (Hằng đẳng thức bạn ạ)

C2:        \(4x^2-4x+1\)

           =\(4x^2-2x-2x+1\)

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

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

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

Mình chắc 100% đó .     **** mình bạn na !!!

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

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

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

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