$\begin{array}{l}
a)\,\,{x^2} - 8x - {y^2} + 16\\
= \left( {{x^2} - 8x + 16} \right) - {y^2}\\
= {\left( {x - 4} \right)^2} - {y^2}\\
= \left( {x - 4 + y} \right)\left( {x - 4 - y} \right)\\
b)\,\,15 - 2x - {x^2}\\
= 16 - 1 - 2x - {x^2}\\
= 16 - \left( {1 + 2x + {x^2}} \right) = {4^2} - {\left( {1 + x} \right)^2}\\
= \left( {4 + 1 + x} \right)\left( {4 - 1 - x} \right) = \left( {5 + x} \right)\left( {3 - x} \right)\\
c)\,\,\,16x - 5{x^2} - 3\\
= 15x + x - 5{x^2} - 3 = \left( {15x - 5{x^2}} \right) - \left( {3 - x} \right)\\
= 5x\left( {3 - x} \right) - \left( {3 - x} \right) = \left( {3 - x} \right)\left( {5x - 1} \right)\\
d)\,\,{x^2} + 12x + 35\\
= {x^2} + 5x + 7x + 35\\
= x\left( {x + 5} \right) + 7\left( {x + 5} \right) = \left( {x + 5} \right)\left( {x + 7} \right)
\end{array}$
