a: \(4x^{16}+81\)
\(=4x^{16}+81+36x^8-36x^8\)
\(=\left(2x^8+9\right)^2-\left(6x^4\right)^2\)
\(=\left(2x^8+9-6x^4\right)\left(2x^8+9+6x^4\right)\)
c: \(\left(5-y\right)^6-2\cdot\left(125-75y+15y^2-y^3\right)+1\)
\(=\left(5-y\right)^6-2\left(5-y\right)^3+1\)
\(=\left[\left(5-y\right)^3-1\right]^2\)
\(=\left[\left(5-y-1\right)\left[\left(5-y\right)^2+\left(5-y\right)+1\right]\right]^2\)
\(=\left(4-y\right)^2\cdot\left(25-10y+y^2+5-y+1\right)^2\)
\(=\left(y-4\right)^2\cdot\left(y^2-11y+31\right)^2\)
d: \(x^4+2018x^2+2017x+2018\)
\(=x^4+x^3+x^2-x^3-x^2-x+2018x^2+2018x+2018\)
\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2018\right)\)
