\(8x^3y^2+12x^2yz+6xyz+yz=y\left(8x^3y+12x^2z+6xz+z\right)\)
a,
\(81x^4\left(z^2-y^2\right)-z^2+y^2=81x^4\left(z^2-y^2\right)-\left(z^2-y^2\right)\)
\(=\left(z^2-y^2\right)\left(81x^4-1\right)=\left(z-y\right)\left(z+y\right)\left[\left(9x^2\right)^2-1\right]\)
\(=\left(z-y\right)\left(z+y\right)\left(9x^2-1\right)\left(9x^2+1\right)\)
\(=\left(z-y\right)\left(z+y\right)\left(3x-1\right)\left(3x+1\right)\left(9x^2+1\right)\)
c.
\(=\left(\dfrac{x}{2}\right)^3-\left(\dfrac{y}{3}\right)^3+\dfrac{x}{2}-\dfrac{y}{3}\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}\right)+\dfrac{x}{2}-\dfrac{y}{3}\)
\(=\left(\dfrac{x}{2}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{4}+\dfrac{xy}{6}+\dfrac{y^2}{9}+1\right)\)
d.
\(=\left(x^6-y^6\right)+x^4+x^2y^2+y^4\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)+x^4+x^2y^2+y^4\)
\(=\left(x^4+x^2y^2+y^4\right)\left(x^2-y^2+1\right)\)
