Đáp án:
$\begin{array}{l}
1)A = {x^3}.\left( { - \dfrac{5}{4}{x^2}y} \right).\left( {\dfrac{2}{5}{x^3}{y^4}} \right)\\
= \left( { - \dfrac{5}{4}.\dfrac{2}{5}} \right).{x^3}.{x^2}.y.{x^3}.{y^4}\\
= - \dfrac{1}{2}.{x^8}.{y^5}\\
\Rightarrow \left\{ \begin{array}{l}
\text{hệ số}:\dfrac{{ - 1}}{2}\\
\text{Bậc}:13
\end{array} \right.\\
B = \left( { - \dfrac{3}{4}{x^5}{y^4}} \right).\left( {x{y^2}} \right)\left( { - \dfrac{8}{9}{x^2}{y^5}} \right)\\
= \left( { - \dfrac{3}{4}} \right).\left( { - \dfrac{8}{9}} \right).{x^5}{y^4}x{y^2}.{x^2}{y^5}\\
= \dfrac{2}{3}.{x^8}.{y^{11}}\\
\Rightarrow \left\{ \begin{array}{l}
\text{hệ số}:\dfrac{2}{3}\\
\text{Bậc}:19
\end{array} \right.\\
C = \dfrac{{19}}{5}x{y^2}.\left( {{x^3}y} \right).{\left( { - 3{x^{13}}{y^5}} \right)^0}\\
= \dfrac{{19}}{5}.x{y^2}.{x^3}y.1\\
= \dfrac{{19}}{5}{x^4}.{y^3}\\
\Rightarrow \left\{ \begin{array}{l}
\text{hệ số}:\dfrac{{19}}{5}\\
\text{Bậc}:7
\end{array} \right.\\
P = {\left( { - \dfrac{2}{3}{x^3}{y^2}} \right)^2}\left( {\dfrac{1}{2}{x^2}{y^3}} \right)\\
= \dfrac{4}{9}{x^6}{y^4}.\dfrac{1}{2}{x^2}{y^3}\\
= \dfrac{4}{9}.\dfrac{1}{2}.{x^6}{y^4}.{x^2}{y^3}\\
= \dfrac{2}{9}{x^8}{y^7}\\
\Rightarrow \left\{ \begin{array}{l}
\text{hệ số}:\dfrac{2}{9}\\
\text{Bậc}:15
\end{array} \right.\\
B2)a)A = 5xy - 5{x^2} - 2xy + 4xy + 3{x^2} - 2y\\
= - 5{x^2} + 3{x^2} + \left( {5xy - 2xy + 4xy} \right) - 2y\\
= - 2{x^2} + 7xy - 2y\\
x = 3;y = \dfrac{1}{2}\\
\Rightarrow A = - {2.3^2} + 7.3.\dfrac{1}{2} - 2.\dfrac{1}{2}\\
= - 18 + \dfrac{{21}}{2} - 1\\
= - 19 + 10,5\\
= - 8,5\\
B = \dfrac{1}{2}a{b^2} - \dfrac{7}{8}a{b^2} + \dfrac{3}{4}{a^2}b - \dfrac{3}{8}{a^2}b - \dfrac{1}{2}a{b^2}\\
= \left( {\dfrac{1}{2}a{b^2} - \dfrac{7}{8}a{b^2} - \dfrac{1}{2}a{b^2}} \right) + \left( {\dfrac{3}{4}{a^2}b - \dfrac{3}{8}{a^2}b} \right)\\
= \dfrac{{ - 7}}{8}a{b^2} + \dfrac{3}{8}{a^2}b\\
a = - 2;b = - \dfrac{3}{2}\\
\Rightarrow B = - \dfrac{7}{8}.\left( { - 2} \right).{\left( {\dfrac{{ - 3}}{2}} \right)^2} + \dfrac{3}{8}{\left( { - 2} \right)^2}.\left( { - \dfrac{3}{2}} \right)\\
= \dfrac{7}{4}.\dfrac{9}{4} - \dfrac{3}{8}.4.\dfrac{3}{2}\\
= \dfrac{7}{4}.\dfrac{9}{4} - \dfrac{9}{4}\\
= \dfrac{9}{4}.\left( {\dfrac{7}{4} - 1} \right)\\
= \dfrac{9}{4}.\dfrac{3}{4}\\
= \dfrac{{27}}{{16}}\\
C = 2{a^2}b - 8{b^2} + 5{a^2}b + 5{c^2} - 3{b^2} + 4{c^2}\\
= \left( {2{a^2}b + 5{a^2}b} \right) + \left( { - 8{b^2} - 3{b^2}} \right) + \left( {5{c^2} + 4{c^2}} \right)\\
= 7{a^2}b - 11{b^2} + 9{c^2}
\end{array}$
$\begin{array}{l}
a = - 4;b = - 3;c = 2\\
\Rightarrow C = 7.{\left( { - 4} \right)^2}.\left( { - 3} \right) - 11.{\left( { - 3} \right)^2} + {9.2^2}\\
= - 21.16 - 11.9 + 9.4\\
= - 336 - 99 + 36\\
= - 399
\end{array}$
