Đáp án:
$\begin{array}{l}
{111^2} - 22.111 + {11^2}\\
= {111^2} - 2.111.11 + {11^2}\\
= {\left( {111 - 11} \right)^2}\\
= {100^2}\\
= 10000\\
a)\left( {a - b} \right)\left( {a + b} \right)\left( {{a^2} + {b^2}} \right)\left( {{a^4} + {b^4}} \right)\\
= \left( {{a^2} - {b^2}} \right)\left( {{a^2} + {b^2}} \right)\left( {{a^4} + {b^4}} \right)\\
= \left( {{a^4} - {b^4}} \right)\left( {{a^4} + {b^4}} \right)\\
= {a^8} - {b^8}\\
b)2\left( {a + 1} \right)\left( {a - 1} \right) + {\left( {a + 1} \right)^2} + {\left( {a - 1} \right)^2}\\
= {\left( {a + 1} \right)^2} + 2\left( {a + 1} \right)\left( {a - 1} \right) + {\left( {a - 1} \right)^2}\\
= {\left( {a + 1 + a - 1} \right)^2}\\
= {\left( {2a} \right)^2}\\
= 4{a^2}
\end{array}$
