a: \(=x^2\left(x-y\right)+2014\left(x-y\right)=\left(x-y\right)\left(x^2+2014\right)\)

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

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

`=(-x-2)^2`

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

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

\(x^4+2015x^2+2014x+2015.\)

=\(\left(x^4-x\right)+2015x^2+2015x+2015\)

=\(x\left(x^3-1\right)+2015\left(x^2+x+1\right)\)

=\(x\left(x-1\right)\left(x^2+x+1\right)+2015\left(x^2+x+1\right)\)

= \(\left(x^2+x+1\right)\left(x^2-x-2015\right)\)

k cho mik

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

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

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

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

Đề lỗi hay sao í bạn. Bạn xem lại đề!

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

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

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

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

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