Đáp án:
$\begin{array}{l}
B1)\\
a){83^2} + 34.83 + {17^2}\\
= {83^2} + 2.17.83 + {17^2}\\
= {\left( {83 + 17} \right)^2}\\
= {100^2}\\
= 10000\\
B2)\\
a){x^2} - 25\\
= {x^2} - {5^2}\\
= \left( {x - 5} \right)\left( {x + 5} \right)\\
b){x^2} - xy + x\\
= x.\left( {x - y + 1} \right)\\
c){x^2} + 2{x^2}y + x{y^2} - 4x\\
= x\left( {x + 2xy + {y^2} - 4} \right)\\
d)4 - {x^2} - 2xy - {y^2}\\
= 4 - \left( {{x^2} + 2xy + {y^2}} \right)\\
= 4 - {\left( {x + y} \right)^2}\\
= \left( {2 - x - y} \right)\left( {2 + x + y} \right)\\
3)\\
a){\left( {x - 2} \right)^2} - 5x + 10 = 0\\
\Rightarrow {\left( {x - 2} \right)^2} - 5\left( {x - 2} \right) = 0\\
\Rightarrow \left( {x - 2} \right)\left( {x - 2 - 5} \right) = 0\\
\Rightarrow \left( {x - 2} \right)\left( {x - 7} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 2\\
x = 7
\end{array} \right.\\
\text{Vậy}\,x = 2;x = 7\\
b){\left( {2x - 3} \right)^2} - {\left( {x - 1} \right)^2} = 0\\
\Rightarrow \left( {2x - 3 - x + 1} \right)\left( {2x - 3 + x - 1} \right) = 0\\
\Rightarrow \left( {x - 2} \right)\left( {3x - 4} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 2\\
x = \frac{4}{3}
\end{array} \right.\\
\text{Vậy}\,x = 2;x = \frac{4}{3}
\end{array}$
