a.\(27x^3+27x^2+9x+1=\left(3x+1\right)^3\)

b.\(x^3-6x^2+12x-8=\left(x-2\right)^3\)

c.\(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

a)  \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)

b)  \(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

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

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

a. \(=6.\left(x^2+2x+1\right)=6\left(x+1\right)^2\)

b. \(=8x^2-6x+4x-3=2x\left(4x-3\right)+\left(4x-3\right)=\left(2x+1\right)\left(4x-3\right)\)

c. \(=8x^2+6x-4x-3=2x\left(4x+3\right)-\left(4x+3\right)=\left(2x-1\right)\left(4x+3\right)\)

1. \(x^3+2x^2-6x-27=\left(x-3\right)\left(x^2+5x+9\right)\)

2. \(9x^2+6x-4y^2-4y=\left(9x^2-4y^2\right)+\left(6x-4y\right)\)

\(=\left(3x-2y\right)\left(3x+2y\right)+2\left(3x-2y\right)=\left(3x-2y\right)\left(3x+2y+2\right)\)

3. \(12x^3+4x^2-27x-9=4x^2\left(3x+1\right)-9\left(3x+1\right)\)

\(=\left(3x+1\right)\left(x^2-\dfrac{9}{4}\right)=\left(x+\dfrac{1}{3}\right)\left(x+\dfrac{3}{2}\right)\left(x-\dfrac{3}{2}\right)\)

1) Ta có: \(x^3+2x^2-6x-27\)

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

\(=\left(x-3\right)\left(x^2+5x+9\right)\)

2: Ta có: \(9x^2+6x-4y^2-4y\)

\(=\left(3x-2y\right)\left(3x+2y\right)+2\left(3x-2y\right)\)

\(=\left(3x-2y\right)\left(3x+2y+2\right)\)

\(8x^3-12x^2+6x-9\\ =4x^2\left(2x-3\right)+3\left(2x-3\right)\\ =\left(2x-3\right)\left(4x^2+3\right)\)

\(-x^2+9x-1+4y^2\\ =-\left(x^2-9x+1-4y^2\right)\)

a) \(27x^3+27x^2+9x+1=\left(3x+1\right)^3\)

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

c) \(-8+12x-6x^2+x^3=\left(x-2\right)^3\)

\(8x^3+12x^2+6x+1\)

\(=\left(2x\right)^3-3\left(2x\right)^2.1+2.3x.1^2-1^3\)

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