Đáp án:
$\begin{array}{l}
3a){\left( {x + 2} \right)^2} + {\left( {x - 2} \right)^2}\\
= {x^2} + 4x + 4 + {x^2} - 4x + 4\\
= 2{x^2} + 8\\
b){\left( {x - 3} \right)^2} - {\left( {x + 2} \right)^2}\\
= \left( {x - 3 + x + 2} \right)\left( {x - 3 - x - 2} \right)\\
= \left( {2x - 1} \right).\left( { - 5} \right)\\
= 5 - 10x\\
c)\left( {x - 4} \right)\left( {{x^2} + 4x + 16} \right) - x\left( {{x^2} - 3} \right)\\
= {x^3} - {4^3} - {x^3} + 3x\\
= 3x - 64\\
d)\left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) - x\left( {{x^2} + 2} \right)\\
= {x^3} + 27 - {x^3} - 2x\\
= 27 - 2x\\
e)\left( {x + 5} \right)\left( {x - 7} \right) - {\left( {x - 2} \right)^2}\\
= {x^2} - 7x + 5x - 35 - {x^2} + 4x - 4\\
= 2x - 39\\
g){\left( {x + y} \right)^2} + 2\left( {x + y} \right)\left( {x - y} \right) + {\left( {x - y} \right)^2}\\
= {\left( {x + y + x - y} \right)^2}\\
= {\left( {2x} \right)^2}\\
= 4{x^2}\\
4)a){x^2} + 2x + 1 = {\left( {x + 1} \right)^2} = {\left( {99 + 1} \right)^2} = 10000\\
b){x^2} - 2x + 1 = {\left( {x - 1} \right)^2} = {\left( {101 - 1} \right)^2} = 10000\\
c){x^3} + 3{x^2}y + 3x{y^2} + {y^3}\\
= {\left( {x + y} \right)^3}\\
= {\left( {34 + 16} \right)^3}\\
= {50^3} = 125000\\
5)A = {x^2} + 4x + 9\\
= {\left( {x + 2} \right)^2} + 5 \ge 5\\
\Leftrightarrow GTNN:A = 5\,khi:x = - 2
\end{array}$
