\[\begin{array}{l}
a)\,\,49{x^2} - {y^6} = {\left( {7x} \right)^2} - {\left( {{y^3}} \right)^2} = \left( {7x - {y^3}} \right)\left( {7x + {y^3}} \right).\\
b)\,\,{x^4} + 1 - 2{x^2} = {\left( {{x^2} - 1} \right)^2} = {\left( {x - 1} \right)^2}{\left( {x + 1} \right)^2}.\\
c)\,\,\, - {x^3} + 3{x^2} - 3x + 1 = {\left( {1 - x} \right)^3}\\
d)\,\,9{x^2} + 12x + 4 = {\left( {3x + 2} \right)^2}\\
e)\,\,\frac{1}{{27{x^3}}} + {y^3} = \left( {\frac{1}{{3x}} + y} \right)\left( {\frac{1}{{9{x^2}}} - \frac{y}{{3x}} + {y^2}} \right).\\
f)\,{\left( {a - b} \right)^3} - {\left( {a + b} \right)^3} = \left( {a - b - a - b} \right)\left( {a - b + a + b} \right) = - 2b.2a = - 4ab.
\end{array}\]
