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

Bài 4:

a) Ta có: \(x^3+6x^2+12x+8\)

\(=x^3+2x^2+4x^2+8x+4x+8\)

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

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

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

b) Ta có: \(x^3-3x^2+3x-1\)

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

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

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

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

c) Ta có: \(1-9x+27x^2-27x^3\)

\(=1-3x-6x+18x^2+9x^2-27x^3\)

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

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

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

d) Ta có: \(x^3+\frac{3}{2}x^2+\frac{3}{4}x+\frac{1}{8}\)

\(=x^3+3\cdot x^2\cdot\frac{1}{2}+3\cdot x\cdot\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3\)

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

e) Ta có: \(27x^3-54x^2y+36xy^2-8y^3\)

\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot2y+3\cdot3x\cdot\left(2y\right)^2-\left(2y\right)^3\)

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

a) \(x^3+6x^2+12x+8\)

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

b) \(x^3-3x^2+3x-1\)

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

c) \(1-9x+27x^2-27x^3\)

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

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

d) \(x^3+\frac{3}{2}x^2+\frac{3}{4}x+\frac{1}{8}\)

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

e) \(27x^3-54x^2y+36xy^2-8y^3\)

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

a) x^3+6x^2+12x+8
=(x+2)^3
b)x^3-3x^2+3x-1
=(x-1)^3
c)1-9x+27x^2-27x^3
=(1-3x)^3
d)x^3+3/2x^2+3/4x+1/8
=(x+1/2)^3
e)27x^3-54x^2y+36xy^2-8y^3
=(3x-2y)^3
Chúc cậu học tốt!and......mình làm hơi tắt cậu làm đầy đủ nha!Cảm ơn!

a,  x^3 +3.3.x^2+3.3^2.x+3^3

= (x+3)^3.

b , 2³-3*x*2²+3*x²*2-x³

<=> (2-x)³

c, (x²)³-3*(x²)²*x+3*x²*x²-x³

<=> (x²-x)³

Bài 1:

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

\(=\left(\dfrac{1}{3}x\right)^2-2\cdot\dfrac{1}{3}x\cdot3+3^2=\left(\dfrac{1}{2}x-3\right)^2\)

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

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

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