Đáp án:
$\begin{array}{l}
43)a)100{x^2} - {\left( {{x^2} + 25} \right)^2}\\
= \left( {10x - {x^2} - 25} \right)\left( {10x + {x^2} + 25} \right)\\
= - {\left( {x - 5} \right)^2}{\left( {x + 5} \right)^2}\\
b){\left( {x - y + 5} \right)^2} - 2\left( {x - y + 5} \right) + 1\\
= {\left( {x - y + 5 - 1} \right)^2}\\
= {\left( {x - y - 4} \right)^2}\\
44){\left( {{x^2} + 4{y^2} - 5} \right)^2} - 16\left( {{x^2}{y^2} + 2xy + 1} \right)\\
= {\left( {{x^2} + 4{y^2} - 5} \right)^2} - 16{\left( {xy + 1} \right)^2}\\
= \left( {{x^2} + 4{y^2} - 5 - 4xy - 4} \right)\left( {{x^2} + 4{y^2} - 5 + 4xy + 4} \right)\\
= \left( {{x^2} + 4{y^2} - 4xy - 9} \right)\left( {{x^2} + 4{y^2} + 4xy - 1} \right)\\
= \left[ {{{\left( {x - 2y} \right)}^2} - 9} \right].\left[ {{{\left( {x + 2y} \right)}^2} - 1} \right]\\
= \left( {x - 2y - 3} \right)\left( {x - 2y + 3} \right)\\
\left( {x + 2y - 1} \right)\left( {x + 2y + 1} \right)
\end{array}$
