\begin{tabular}{l} Factorise the following expression \\ completely: \\ \( \qquad 16-y^{8} \) \\ Answer: \\ \hline\end{tabular}

Factor the expression \( 16-y^{8} \). Factor the expression by following steps: - step0: Factor: \(16-y^{8}\) - step1: Rewrite the expression: \(\left(16^{\frac{1}{2}}\right)^{2}-\left(y^{4}\right)^{2}\) - step2: Factor the expression: \(\left(16^{\frac{1}{2}}-y^{4}\right)\left(16^{\frac{1}{2}}+y^{4}\right)\) - step3: Evaluate: \(\left(4-y^{4}\right)\left(16^{\frac{1}{2}}+y^{4}\right)\) - step4: Evaluate: \(\left(4-y^{4}\right)\left(4+y^{4}\right)\) - step5: Evaluate: \(\left(2-y^{2}\right)\left(2+y^{2}\right)\left(4+y^{4}\right)\) - step6: Factor the expression: \(\left(2-y^{2}\right)\left(2+y^{2}\right)\left(y^{2}-2y+2\right)\left(y^{2}+2y+2\right)\) The complete factorization of the expression \(16-y^{8}\) is \((2-y^{2})(2+y^{2})(y^{2}-2y+2)(y^{2}+2y+2)\).