Đáp án:
$\begin{array}{l}
1)\\
+ ){\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\\
{\left( {b + a} \right)^2} = {b^2} + 2ab + {a^2}\\
\Leftrightarrow {\left( {a + b} \right)^2} = {\left( {b + a} \right)^2}\\
+ ){\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\\
{\left( {b - a} \right)^2} = {b^2} - 2ab + {a^2}\\
\Leftrightarrow {\left( {a - b} \right)^2} = {\left( {b - a} \right)^2}\\
2)a + b = 5;a.b = 6\\
M = {\left( {a + b} \right)^2} = {5^2} = 25\\
N = {a^2} + {b^2} + 5ab\\
= {a^2} + 2ab + {b^2} + 3ab\\
= {\left( {a + b} \right)^2} + 3ab\\
= {5^2} + 3.6 = 25 + 18 = 43\\
P = {a^2} + {b^2} - 4ab\\
= {a^2} + 2ab + {b^2} - 6ab\\
= {\left( {a + b} \right)^2} - 6ab\\
= {5^2} - 6.6\\
= 25 - 36\\
= - 11\\
Q = \dfrac{a}{b} + \dfrac{b}{a}\\
= \dfrac{{{a^2} + {b^2}}}{{ab}}\\
= \dfrac{{{{\left( {a + b} \right)}^2} - 2ab}}{{ab}}\\
= \dfrac{{{5^2} - 2.6}}{6}\\
= \dfrac{{25 - 12}}{6} = \dfrac{{13}}{6}\\
H = {a^3}{b^2} + {a^2}{b^3}\\
= {a^2}{b^2}\left( {a + b} \right)\\
= {6^2}.5 = 36.5 = 180
\end{array}$
