Đáp án:
$\begin{array}{l}
1)A = \left( {3x - 5} \right)\left( {3x + 5} \right) - 9{x^2}\\
= {\left( {3x} \right)^2} - {5^2} - 9{x^2}\\
= 9{x^2} - 25 - 9{x^2}\\
= - 25\\
B = x\left( {x - 4} \right) - \left( {x - 2} \right)\left( {x + 2} \right)\\
= {x^2} - 4x - \left( {{x^2} - 4} \right)\\
= {x^2} - 4x - {x^2} + 4\\
= - 4x + 4\\
C = {\left( {x + 8} \right)^2} - x\left( {x + 16} \right)\\
= {x^2} + 16x + 64 - {x^2} - 16x\\
= 64\\
D = \left( {x + 7} \right)\left( {x - 7} \right) - {\left( {x - 1} \right)^2}\\
= {x^2} - 49 - \left( {{x^2} - 2x + 1} \right)\\
= 2x - 50\\
B2)A = {x^2} + 20x + 3\\
= {x^2} + 2.x.10 + 100 - 97\\
= {\left( {x + 10} \right)^2} - 97 \ge - 97\\
\Leftrightarrow GTNN:A = - 97\,khi:x = - 10\\
B = {x^2} - 12x - 1\\
= {x^2} - 2.x.6 + 36 - 37\\
= {\left( {x - 6} \right)^2} - 37 \ge - 37\\
\Leftrightarrow GTNN:B = - 37\,khi:x = 6\\
B3)A = - {x^2} + 14x - 3\\
= - \left( {{x^2} - 14x} \right) - 3\\
= - \left( {{x^2} - 2.x.7 + 49} \right) + 49 - 3\\
= - {\left( {x - 7} \right)^2} + 46 \le 46\\
\Leftrightarrow GTLN:A = 46\,khi:x = 7\\
B = - 9{x^2} - 6x + 10\\
= - \left( {9{x^2} + 6x + 1} \right) + 1 + 10\\
= - {\left( {3x + 1} \right)^2} + 11 \le 11\\
\Leftrightarrow GTLN:B = 11\,khi:x = - \frac{1}{3}
\end{array}$
