Đáp án:
$\begin{array}{l}
a){153^2} + 94.153 + {47^2}\\
= {153^2} + 2.47.153 + {47^2}\\
= {\left( {153 + 47} \right)^2}\\
= {200^2}\\
= 40000\\
b){126^2} - 152.126 + {76^2}\\
= {126^2} - 2.76.126 + {76^2}\\
= {\left( {126 - 76} \right)^2}\\
= {50^2}\\
= 2500\\
c)38.58 - \left( {154 - 1} \right)\left( {154 + 1} \right)\\
= \left( {48 - 10} \right)\left( {48 + 10} \right) - {154^2} + 1\\
= {48^2} - {10^2} - {154^2} + 1\\
= - 21511\\
d)\left( {2 + 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)...\left( {{2^{20}} + 1} \right) + 1\\
= \left( {2 - 1} \right)\left( {2 + 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)...\left( {{2^{20}} + 1} \right) + 1\\
= \left( {{2^2} - 1} \right)\left( {{2^2} + 1} \right)\left( {{2^4} + 1} \right)...\left( {{2^{20}} + 1} \right) + 1\\
= \left( {{2^4} - 1} \right)\left( {{2^4} + 1} \right)...\left( {{2^{20}} + 1} \right) + 1\\
= \left( {{2^{20}} - 1} \right)\left( {{2^{20}} + 1} \right) + 1\\
= {2^{40}} - 1 + 1\\
= {2^{40}}
\end{array}$
