Đáp án:
$\begin{array}{l}
a)A = {x^2} + 2xy + {y^2} - 4x - 4y + 3\\
= {\left( {x + y} \right)^2} - 4.\left( {x + y} \right) + 3\\
Thay\,x + y = 3\\
\Rightarrow A = {3^2} - 4.3 + 3\\
= 9 - 12 + 3 = 0\\
Vay\,A = 0\\
b)C = {x^3} - {y^3} - 3xy\\
= \left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right) - 3xy\\
= 1.\left( {{x^2} + xy + {y^2}} \right) - 3xy\left( {do:x - y = 1} \right)\\
= {x^2} - 2xy + {y^2}\\
= {\left( {x - y} \right)^2}\\
= {1^2}\\
= 1\\
Vay\,C = 1\\
c)\left\{ \begin{array}{l}
x + y = m\\
x.y = n
\end{array} \right.\\
A = {x^2} + {y^2}\\
= {x^2} + 2xy + {y^2} - 2xy\\
= {\left( {x + y} \right)^2} - 2xy\\
= {m^2} - 2n\\
B = {x^3} + {y^3}\\
= {\left( {x + y} \right)^3} - 3xy\left( {x + y} \right)\\
= {m^3} - 3mn
\end{array}$
