Đáp án:
$\begin{array}{l}
a)\left( {x - 3} \right)\left( {x + 7} \right) - \left( {x + 5} \right)\left( {x - 1} \right)\\
= {x^2} + 7x - 3x - 21 - \left( {{x^2} - x + 5x - 5} \right)\\
= {x^2} + 4x - 21 - {x^2} - 4x + 5\\
= - 16\\
b){\left( {x + 8} \right)^2} - 2\left( {x + 8} \right)\left( {x - 2} \right) + {\left( {x - 2} \right)^2}\\
= {\left( {x + 8 - \left( {x - 2} \right)} \right)^2}\\
= {\left( {x + 8 - x + 2} \right)^2}\\
= {10^2}\\
= 100\\
c){x^2}\left( {x - 4} \right)\left( {x + 4} \right) - \left( {{x^2} + 1} \right)\left( {{x^2} - 1} \right)\\
= {x^2}\left( {{x^2} - 16} \right) - \left( {{x^4} - 1} \right)\\
= {x^4} - 16{x^2} - {x^4} + 1\\
= - 16{x^2} + 1\\
d)\left( {x + 1} \right)\left( {{x^2} - x + 1} \right) - \left( {x - 1} \right)\left( {{x^2} + x + 1} \right)\\
= {x^3} + 1 - \left( {{x^3} - 1} \right)\\
= 2
\end{array}$
