Đáp án:

$\begin{array}{l}
a)A = {\left( {7x - 4} \right)^2} + {\left( {5x - 4} \right)^2} + 2\left( {7x - 4} \right)\left( {5x - 4} \right)\\
 = {\left( {7x - 4 + 5x - 4} \right)^2}\\
 = {\left( {12x - 8} \right)^2}\\
 = 144{x^2} - 192x + 64\\
b)B = \left( {2{a^2} + 2a + 1} \right){\left( {2{a^2} - 2a + 1} \right)^2} - {\left( {2{a^2} + 1} \right)^2}\\
 = {\left( {2{a^2} + 1} \right)^2} - {\left( {2a} \right)^2} - {\left( {2{a^2} + 1} \right)^2}\\
 =  - 4{a^2}\\
c)C = \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) - \left( {54 + {x^3}} \right)\\
 = {x^3} + 27 - 54 - {x^3}\\
 =  - 27\\
d)D = \left( {2x + y} \right)\left( {4{x^2} - 2xy + {y^2}} \right)\\
 - \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)\\
 = {\left( {2x} \right)^3} + {y^3} - \left( {8{x^3} - {y^3}} \right)\\
 = 2{y^3}\\
e)E = {\left( {a + b} \right)^2} - {\left( {a - b} \right)^2}\\
 = \left( {a + b + a - b} \right)\left( {a + b - a + b} \right)\\
 = 2a.2b\\
 = 4ab\\
f)F = {\left( {2x + 3y + 1} \right)^2} - {\left( {2x - 3y - 1} \right)^2} - 24xy\\
 = \left( {2x + 3y + 1 + 2x - 3y - 1} \right)\left( {2x + 3y + 1 - 2x + 3y + 1} \right)\\
 - 24xy\\
 = 4x.\left( {6y + 2} \right) - 24xy\\
 = 24xy + 8x - 24xy\\
 = 8x\\
g)G = {\left( {a + b} \right)^3} - {\left( {a - b} \right)^3} - 2{b^3}\\
 = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}\\
 - {a^3} + 3{a^2}b - 3a{b^2} + {b^3} - 2{b^3}\\
 = 6{a^2}b\\
h)\\
H = {\left( {2x + y} \right)^3} + {\left( {2x - y} \right)^3}\\
 + 3\left( {2x + y} \right)\left( {4{x^2} - {y^2}} \right)\\
 + 3\left( {2x - y} \right)\left( {4{x^2} - {y^2}} \right)\\
 = {\left( {2x + y} \right)^3} + {\left( {2x - y} \right)^3}\\
 + 3{\left( {2x + y} \right)^2}\left( {2x - y} \right)\\
 + 3\left( {2x + y} \right){\left( {2x - y} \right)^2}\\
 = {\left( {2x + y + 2x - y} \right)^3}\\
 = {\left( {4x} \right)^3}\\
 = 64{x^3}
\end{array}$