\(\begin{array}{l}8{x^3} - 36{x^2}y + 54x{y^2} - 27{y^3}\\ = {\left( {2x} \right)^3} - 3.{\left( {2x} \right)^2}.3y + 3.\left( {2x} \right).{\left( {3y} \right)^2} - {\left( {3y} \right)^3}\\ = {\left( {2x - 3y} \right)^3}\end{array}\)

a)      \(27 + 54x + 36{x^2} + 8{x^3} = {3^3} + {3.3^2}.2x + 3.3.{\left( {2x} \right)^2} + {\left( {2x} \right)^3} = {\left( {3 + 2x} \right)^3}\)

b)      \(64{x^3} - 144{x^2}y + 108x{y^2} - 27{y^3} = {\left( {4x} \right)^3} - 3.{\left( {4x} \right)^2}.3y + 3.4x.{\left( {3y} \right)^2} - {\left( {3y} \right)^3} = {\left( {4x - 3y} \right)^3}\)

Ta có 8 x 3   +   36 x 2   +   54 x   +   27   =   ( 2 x ) 3   +   3 ( 2 x ) 2 . 3   +   3 . 2 x . 3 2   +   3 3   =   ( 2 x   +   3 ) 3

Đáp án cần chọn là: B

a) \(A=8x^3+12x^2y+6xy^2+y^3=\left(2x+y\right)^3\)

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

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

d)  \(D=27+27y^2+9y^4+y^6=\left(3+y^2\right)^3\)

a, \(\dfrac{27}{8x^3-1}:\dfrac{3}{2x-1}\)

\(=\dfrac{27}{\left(2x-1\right)\left(4x^2+2x+1\right)}.\dfrac{2x-1}{3}\)

\(=\dfrac{9}{4x^2+2x+1}\)

b, \(\dfrac{8x^3+36x^2+54x+27}{2x+3}=\dfrac{\left(2x+3\right)^3}{2x+3}=\left(2x+3\right)^2\)

a) Sửa đề: \(8x^3+36x^2+54x+27\)

Ta có: \(8x^3+36x^2+54x+27\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2+3^3\)

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

b) Ta có: \(x^2+4x+4\)

\(=x^2+2\cdot x\cdot2+2^2\)

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

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

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

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

\(8x^3-36x^2+54x-27\)

\(=\left(2x\right)^3-3.\left(2x\right)^2.3+3.2x.3^2-3^3\)

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