Đáp án:
$\begin{array}{l}
a){\left( {x + y} \right)^2} - {\left( {x - y} \right)^2}\\
= \left( {x + y + x - y} \right)\left( {x + y - x + y} \right)\\
= 2x.2y\\
= 4xy\\
b)5x\left( {x - 2y} \right) + 2{\left( {2y - x} \right)^2}\\
= 5x\left( {x - 2y} \right) + 2{\left( {x - 2y} \right)^2}\\
= \left( {x - 2y} \right)\left( {5x + 2.\left( {x - 2y} \right)} \right)\\
= \left( {x - 2y} \right)\left( {7x - 4y} \right)\\
c)\left( {4x - 8} \right)\left( {{x^2} + 6} \right) - \left( {4x - 8} \right)\left( {x + 7} \right)\\
+ 9\left( {8 - 4x} \right)\\
= \left( {4x - 8} \right)\left( {{x^2} + 6 - x - 7 - 9} \right)\\
= \left( {4x - 8} \right)\left( {{x^2} - x - 10} \right)\\
= 2\left( {x - 2} \right)\left( {{x^2} - x - 10} \right)\\
d)7x{\left( {y - 4} \right)^2} - {\left( {4 - y} \right)^3}\\
= 7x{\left( {y - 4} \right)^2} + {\left( {y - 4} \right)^3}\\
= {\left( {y - 4} \right)^2}\left( {7x + y - 4} \right)
\end{array}$
