\(1-27x^3\)

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

\(=\left(1-3x\right)\left(1+3x+9x^2\right)\)

\(---\)

\(x-3^3+27\)

\(=x-27+27=x\) 

\(---\)

\(27x^3+27x^2+9x+1\)

\(=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3\)

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

\(---\)

\(\dfrac{x^6}{27}-\dfrac{x^4y}{3}+x^2y^2-y^3\) (sửa đề)

\(=\left(\dfrac{x^2}{3}\right)^3-3\cdot\left(\dfrac{x^2}{3}\right)^2\cdot y+3\cdot\dfrac{x^2}{3}\cdot y^2-y^3\)

 \(=\left(\dfrac{x^2}{3}-y\right)^3\)

#Ayumu

1-27x\(^3\)

=(1-3x)(1+3x+9x\(^2\)

    x³ - x² + 3x - 27.

= (x³ - 27) - (x² - 3x).

= (x - 3) (x² + 3x + 9) - x (x - 3).

= (x - 3) (x² + 3x + 9 - x).

= (x - 3) (x² + 2x + 9).

x³ - x² + 3x - 27 = ( x³ - 27 ) - ( x² - 3x )

= ( x - 3 ) ( x² + 3x + 9 ) - x ( x - 3 ) 

= ( x - 3 ) ( x² + 3x + 9 - x )

= ( x - 3 ) ( x² - 2x + 9 )

* Chúc bạn học tốt

x³+27+(x+3)(x+9)

=x³+3³+(x+3)(x+9)

=(x+3)(x²-3x+9)+(x+3)(x+9)

=(x+3)(x²-2x+18)

a) \(x^3+2x^2+2x+1\)

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

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

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

b) \(x^3-4x^2+12x-27\)

\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-4x.\left(x-3\right)\)

\(=\left(x-3\right).\left[\left(x^2+3x+9\right)-4x\right]\)

\(=\left(x-3\right).\left(x^2-x+9\right)\)

Đề sai rồi bạn

x³-27+3x(x-3)=(x-3)(x²+3x+9)+3x(x-3)

                   =(x-3)(x²+3x+9+3x)

                   =(x-3)(x²+6x+9)

                  =(x-3)(x+3)²

 x³-27+3x(x-3)=(x-3)(x²+3x+9)+3x(x-3)

                               =(x-3)(x²+3x+9+3x)

                               =(x-3)(x²+6x+9)

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

1.

= (x^3 + 125 ) -(x^2 +5x)

=(x +5) (x^2 -5x +25) -x(x+5)

=(x+5)(x^2 -5x +25 -x)

=(x+5)(x^2 -6x +25)

2.

= (x^3 -27) + (2x^2 -6x)

=(x-3) (x^2 +3x +9) +2x (x-3)

=(x-3) (x^2 +3x +9 +2x)

=(x-3) (x^2 +5x +9)

\(a)-64+y^2=\left(y-8\right)\left(y+8\right)\)

\(b)-27-x^3=-\left(27+x^3\right)=-\left(3+x\right)\left(9-3x+x^2\right)\)

- 64 + y ²

= - 8 . 8 + y . y

= ( y + 8 ) . ( y - 8 ) 

-27 - x³

= - ( 27 + x³ )

= - ( 3 + x ) . ( 9 - 3 + x² )