\(1.\\ a)x^8+x^4+1\\ =\left(x^8+2x^4+1\right)-x^4\\ =\left(x^4+1\right)^2-x^4\\ =\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)
\(2.\\ \left(x+y+z\right)^3-x^3-y^3-z^3\\ =\left(x+y+z-z\right)\left[\left(x+y+z\right)^2+z\left(x+y+z\right)+z^2\right]-\left(x^3+y^3\right)\\ =\left(x+y\right)\left(x^2+y^2+z^2+2xy+2yz+2xz+xz+yz+z^2+z^2\right)-\left(x+y\right)\left(x^2-xy+y^2\right)\\ =\left(x+y\right)\left(x^2+y^2+3z^2+2xy+3yz+3xz-x^2+xy-y^2\right)\\ =\left(x+y\right)\left(3z^2+3xy+3yz+3xz\right)\\ =3\left(x+y\right)\left(xy+xz+yz+z^2\right)\\ 3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\\ =3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
