Đáp án:

$\begin{array}{l}
b){x^2} - 2x + {y^2} - 4y + 7\\
 = {x^2} - 2x + 1 + {y^2} - 4y + 4 + 2\\
 = {\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + 2 \ge 2\\
 \Leftrightarrow GTNN = 2\,khi:x = 1;y = 2\\
c)4{x^2} + 4x\\
 = 4{x^2} + 4x + 1 - 1\\
 = {\left( {2x + 1} \right)^2} - 1 \ge  - 1\\
 \Leftrightarrow GTNN =  - 1\,khi:x =  - \dfrac{1}{2}\\
d)\left( {x - 1} \right)\left( {x + 2} \right)\left( {x + 3} \right)\left( {x + 6} \right)\\
 = \left( {{x^2} + 5x - 6} \right)\left( {{x^2} + 5x + 6} \right)\\
 = {\left( {{x^2} + 5x} \right)^2} - 36 \ge  - 36\\
 \Leftrightarrow GTNN =  - 36\,khi:\left[ \begin{array}{l}
x = 0\\
x =  - 5
\end{array} \right.\\
e)A = 6x - {x^2} + 5\\
 =  - \left( {{x^2} - 6x + 9} \right) + 9 + 5\\
 =  - {\left( {x - 3} \right)^2} + 14 \le 14\\
 \Leftrightarrow GTLN:A = 14\,khi:x = 3\\
B2)\\
a){\left( {x + y} \right)^2} - {y^2}\\
 = \left( {x + y + y} \right)\left( {x + y - y} \right)\\
 = x\left( {x + 2y} \right)\\
b){\left( {{x^2} + {y^2}} \right)^2} - {\left( {2xy} \right)^2}\\
 = \left( {{x^2} + {y^2} + 2xy} \right)\left( {{x^2} + {y^2} - 2xy} \right)\\
 = {\left( {x + y} \right)^2}{\left( {x - y} \right)^2}\\
c){\left( {x + y} \right)^3} - \left( {{x^3} + {y^3}} \right)\\
 = {x^3} + 3{x^2}y + 3x{y^2} + {y^3} - {x^3} - {y^3}\\
 = 3xy\left( {x + y} \right)\\
d){\left( {a + b} \right)^2} + 2\left( {a + b} \right)\left( {a - b} \right) + {\left( {a - b} \right)^2}\\
 = {\left( {a + b + a - b} \right)^2}\\
 = {\left( {2a} \right)^2}\\
 = 4{a^2}\\
e){\left( {a + b + c} \right)^2} + {\left( {b + c - a} \right)^2} + {\left( {c + a - b} \right)^2} + {\left( {a + b - c} \right)^2}\\
 = {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ac\\
 + {b^2} + {c^2} + {a^2} + 2bc - 2ab - 2ac\\
 + {c^2} + {a^2} + {b^2} + 2ac - 2bc - 2ab\\
 + {a^2} + {b^2} + {c^2} + 2ab - 2bc - 2ac\\
 = 4\left( {{a^2} + {b^2} + {c^2}} \right)\\
f)\left( {2x + 3} \right)\left( {4{x^2} + 9} \right)\left( {2x - 3} \right)\\
 = \left( {2x + 3} \right)\left( {2x - 3} \right)\left( {4{x^2} + 9} \right)\\
 = \left( {4{x^2} - 9} \right)\left( {4{x^2} + 9} \right)\\
 = 16{x^4} - 81
\end{array}$