\(a,x^3+6x^2+12x+8=x^3+2x^2+4x^2+8x+4x+8\\ =x^2\left(x+2\right)+8x\left(x+2\right)+4\left(x+2\right)\\ =\left(x^2+8x+4\right)\left(x+2\right)\\ b,x^3-3x^2+3x-1=\left(x-1\right)^3\\ c,1-9x+27x^2-27x^3\\ =1^3-3.1^2.3x+3.1.\left(3x\right)^2-\left(3x\right)^3\\ =\left(1-3x\right)^3\)
\(d,x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}\\ =x^3+3.x^2.\dfrac{1}{2}+3.x.\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3\\ =\left(x+\dfrac{1}{2}\right)^3\\ e,27x^3-54x^2y+36xy^2-8y^3\\ =\left(27x^3-8y^3\right)-54x^2y+36xy^2\\ =\left[\left(3x\right)^3-\left(2y\right)^3\right]-18xy\left(3x+2y\right)\\ =\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)+18xy\left(2y-3x\right)\\ =\left(3x-2y\right)\left(9x^2+6xy+18xy+4y^2\right)\\ =\left(3x-2y\right)\left(9x^2+24xy+4y^2\right)\)
