Đáp án:
$\begin{array}{l}
a)E = {\left( {2x + 3} \right)^2} - 2\left( {2x + 3} \right)\left( {2x + 5} \right) + {\left( {2x + 5} \right)^2}\\
= {\left( {2x + 3 - 2x - 5} \right)^2}\\
= {\left( { - 2} \right)^2}\\
= 4\\
b)F = \left( {{x^2} + x + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} - 1} \right)\\
= \left[ {{{\left( {{x^2} + 1} \right)}^2} - {x^2}} \right].\left( {{x^2} - 1} \right)\\
= \left( {{x^4} + 2{x^2} + 1 - {x^2}} \right)\left( {{x^2} - 1} \right)\\
= \left( {{x^4} + {x^2} + 1} \right)\left( {{x^2} - 1} \right)\\
= {\left( {{x^2}} \right)^3} - 1\\
= {x^6} - 1\\
c)G = {\left( {a + b - c} \right)^2} + {\left( {a - b + c} \right)^2} - 2{\left( {b - c} \right)^2}\\
= {a^2} + 2.a.\left( {b - c} \right) + {\left( {b - c} \right)^2}\\
+ {a^2} - 2.a.\left( {b - c} \right) + {\left( {b - c} \right)^2} - 2{\left( {b - c} \right)^2}\\
= 2{a^2}\\
d)H = {\left( {a + b + c} \right)^2} + {\left( {a - b - c} \right)^2}\\
+ {\left( {b - c - a} \right)^2} + {\left( {c - a - b} \right)^2}\\
= {a^2} + 2a\left( {b + c} \right) + {\left( {b + c} \right)^2}\\
+ {a^2} - 2a\left( {b + c} \right) + {\left( {b + c} \right)^2}\\
+ {a^2} + 2a\left( {b - c} \right) + {\left( {b - c} \right)^2}\\
+ {a^2} - 2a\left( {b - c} \right) + {\left( {b - c} \right)^2}\\
= 4{a^2} + 2{\left( {b + c} \right)^2} + 2{\left( {b - c} \right)^2}\\
= 4{a^2} + 4{b^2} + 4{c^2}
\end{array}$
