Đáp án:
$\begin{array}{l}
a){a^3} - 3{a^2}b + 3a{b^2} - {b^3}\\
= {\left( {a - b} \right)^3}\\
b)25 - {a^2} - 2ab - {b^2}\\
= 25 - \left( {{a^2} + 2ab + {b^2}} \right)\\
= {5^2} - {\left( {a + b} \right)^2}\\
= \left( {5 - a - b} \right)\left( {5 + a + b} \right)\\
c)4{x^2} - 25 + \left( {2x + 7} \right)\left( {5 - 2x} \right)\\
= \left( {2x - 5} \right)\left( {2x + 5} \right) - \left( {2x - 5} \right)\left( {2x + 7} \right)\\
= \left( {2x - 5} \right)\left( {2x + 5 - 2x - 7} \right)\\
= - 2.\left( {2x - 5} \right)\\
= 2\left( {5 - 2x} \right)\\
d){x^2} - 2014x + 2013\\
= {x^2} - x - 2013x + 2013\\
= x\left( {x - 1} \right) - 2013\left( {x - 1} \right)\\
= \left( {x - 1} \right)\left( {x - 2013} \right)\\
e){a^2}{x^2} - {a^2}{y^2} - {b^2}{x^2} + {b^2}{y^2}\\
= {a^2}\left( {{x^2} - {y^2}} \right) - {b^2}\left( {{x^2} - {y^2}} \right)\\
= \left( {{x^2} - {y^2}} \right)\left( {{a^2} - {b^2}} \right)\\
= \left( {x - y} \right)\left( {x + y} \right)\left( {a - b} \right)\left( {a + b} \right)\\
f){x^2} - {y^2} + 12y - 36\\
= {x^2} - \left( {{y^2} - 12y + 36} \right)\\
= {x^2} - {\left( {y - 6} \right)^2}\\
= \left( {x - y + 6} \right)\left( {x + y - 6} \right)\\
g){\left( {x + 2} \right)^2} - {x^2} + 2x - 1\\
= {\left( {x + 2} \right)^2} - {\left( {x - 1} \right)^2}\\
= \left( {x + 2 - x + 1} \right)\left( {x + 2 + x - 1} \right)\\
= 3.\left( {2x + 1} \right)\\
h)16{x^2} - {y^2}\\
= \left( {4x + y} \right)\left( {4x - y} \right)
\end{array}$
