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

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

`=(-x-2)^2`

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

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

Đề lỗi hay sao í bạn. Bạn xem lại đề!

Ta có \(\left(1+2x\right)\left(1-2x\right)-x\left(x+2\right)\left(x-2\right)\)

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

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

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

= 1 - 4x² - ( x² - 4)

= 1 - 4x² - x² + 4

= -5x² + 5

= - ( 5x² - 5 )

= - 5 (x² - 1)

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

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

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

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

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

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

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

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

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

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

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

Chúc bạn học tốt.

x(x+2)(x^2+2x+2)+1

(x^2+2x)(x^2+2x+2)+1

dat x^2+2x=a

=> a(a+2)+1

=a^2+2a+1

=(a+1)^2

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

=(x+1)^4 

x(x+2)(x^2+2x+2)+1

(x^2+2x)(x^2+2x+2)+1

dat x^2+2x=a

=> a(a+2)+1

=a^2+2a+1

=(a+1)^2

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

=(x+1)^4 

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

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

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