Đáp án:
$\begin{array}{l}
1)a){142^2} + 116.142 + {58^2}\\
= {142^2} + 2.142.58 + {58^2}\\
= {\left( {142 + 58} \right)^2}\\
= {200^2}\\
= 40000\\
b){124^2} + {24^2} - 124.48\\
= {124^2} - 2.124.24 + {24^2}\\
= {\left( {124 - 24} \right)^2}\\
= {100^2}\\
= 10000\\
c)27{x^3} + 27{x^2} + 9x\\
= {\left( {3x} \right)^3} + 3.9{x^2}.1 + 3.3x{.1^2} + 1 - 1\\
= {\left( {3x + 1} \right)^3} - 1\\
= {\left( {3.33 + 1} \right)^3} - 1\\
= {100^3} - 1\\
= 1000000 - 1\\
= 999999\\
e)\left( {{{20}^2} + {{18}^2} + {{16}^2} + ... + {4^2} + {2^2}} \right)\\
- \left( {{{19}^2} + {{17}^2} + ... + {3^2} + {1^2}} \right)\\
= {20^2} - {19^2} + {18^2} - {17^2} + ... + {4^2} - {3^2} + {2^2} - {1^2}\\
= \left( {20 - 19} \right)\left( {20 + 19} \right) + \left( {18 - 17} \right)\left( {18 + 17} \right)\\
+ ... + \left( {4 - 3} \right)\left( {4 + 3} \right) + \left( {2 - 1} \right)\left( {2 + 1} \right)\\
= 20 + 19 + 18 + 17 + ... + 4 + 3 + 2 + 1\\
= \frac{{\left( {20 + 1} \right).20}}{2}\\
= 210\\
B2)b){\left( {x + y} \right)^2} - {\left( {x - y} \right)^2}\\
= \left( {x + y + x - y} \right)\left( {x + y - x + y} \right)\\
= 2x.2y\\
= 4xy
\end{array}$
