a: \(A=\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)+3\left(x-1\right)\left(x^2+x+1\right)+3\left(x-1\right)^2-x-5\)
\(=x^3-3x^2+3x-1+3\left(x^3-1\right)-4x\left(x^2-1\right)+3\left(x^2-2x+1\right)-x-5\)
\(=4x^3-3x^2+3x-4-4x^3+4x+3x^2-6x+3-x-5\)
\(=-6\)
b: \(B=\left(2x+\dfrac{1}{3}y\right)\left(4x^2-\dfrac{2}{3}xy+\dfrac{1}{9}y^2\right)-\left(8x^3+\dfrac{1}{27}y^3\right)\)
\(=\left(2x+\dfrac{1}{3}y\right)\left[\left(2x\right)^2-2x\cdot\dfrac{1}{3}y+\left(\dfrac{1}{3}y\right)^2\right]-8x^3-\dfrac{1}{27}y^3\)
\(=8x^3+\dfrac{1}{27}y^3-8x^3-\dfrac{1}{27}y^2=0\)
c: \(C=\left(x-y\right)^3-\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\left(y-x\right)-1\)
\(=x^3-3x^2y+3xy^2-y^3-x^3+y^3-3xy^2+3x^2y-1\)
=-1
d: \(D=8x\left(x-2\right)\left(x+2\right)-\left(2x+3\right)\left(4x^2+6x+9\right)+3x\left(x-1\right)\)
\(=8x\left(x^2-4\right)-8x^3-27+3x^2-3x\)
\(=8x^3-32x-8x^3+3x^2-3x-27\)
\(=3x^2-35x-27\)
