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)

Lần sau bạn cần chú ý viết đầy đủ yêu cầu đề bài.

Coi đây là bài toán rút gọn/ khai triển.

Ta có:

$(1+2x)(1-2x)-x(x+2)(x-2)$

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

$=1-4x^2-x(x^2-4)=-x^3-4x^2+4x+1$

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

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

\(=-x^3+x^2-5x^2+5x-x+1\)

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

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

\(=\left(1-x\right)\left(x^2+\dfrac{2x.5}{2}+\dfrac{25}{4}-\dfrac{21}{4}\right)\)

\(=\left(1-x\right)\left(\left(x+\dfrac{5}{2}\right)^2-\dfrac{21}{4}\right)\)

\(=\left(1-x\right)\left(x+\dfrac{5}{2}-\dfrac{\sqrt{21}}{2}\right)\left(x+\dfrac{5}{2}+\dfrac{\sqrt{21}}{2}\right)\)

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

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

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

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

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

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

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

Chúc bạn học tốt.

1) \(x\left(4x+1\right)\)

2) \(3\left(x-3y\right)\)

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

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

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

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

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

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

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

x³ + 2x² + 2x + 1 

= (x³ + 1) + (2x² + 2x)

= (x + 1)(x² + x + 1) + 2x(x + 1)

= (x + 1)(x² + x + 1 + 2x)

= (x + 1)(x² + 3x + 1)

 Chúc bạn học tốt

Ta có: \(x^3+2x^2+2x+1\)

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

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

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