Đáp án:
$\begin{array}{l}
a)\\
A = {\left( {x + 5} \right)^2} - 4x{\left( {2x + 3} \right)^2} - \left( {2x - 1} \right)\left( {x + 3} \right)\left( {x - 3} \right)\\
= {x^2} + 10x + 25 - 4x\left( {4{x^2} + 12x + 9} \right)\\
- \left( {2x - 1} \right)\left( {{x^2} - 9} \right)\\
= {x^2} + 10x + 25 - 16{x^3} - 48{x^2} - 36x\\
- 2{x^3} + 18x + {x^2} - 9\\
= - 18{x^3} - 46{x^2} - 8x + 16\\
b)\\
B = - 2x\left( {3x + 2} \right)\left( {3x - 2} \right) + 5{\left( {x + 2} \right)^2}\\
- \left( {x - 1} \right)\left( {2x + 1} \right)\left( {2x + 1} \right)\\
= - 2x.\left( {9{x^2} - 4} \right) + 5\left( {{x^2} + 4x + 4} \right)\\
- \left( {x - 1} \right)\left( {4{x^2} + 4x + 1} \right)\\
= - 18{x^3} + 8x + 5{x^2} + 20x + 20\\
- \left( {4{x^3} - 3x - 1} \right)\\
= - 22{x^3} + 5{x^2} + 31x + 21\\
c)\\
C = \left( {7x - 8} \right)\left( {7x + 8} \right) - 10{\left( {2x + 3} \right)^2}\\
+ 5x{\left( {3x - 2} \right)^2} - 4x{\left( {x - 5} \right)^2}\\
= 49{x^2} - 64 - 10\left( {4{x^2} + 12x + 9} \right)\\
+ 5x\left( {9{x^2} - 12x + 4} \right) - 4x\left( {{x^2} - 10x + 25} \right)\\
= 49{x^2} - 64 - 40{x^2} - 120x - 90\\
+ 45{x^3} - 60{x^2} + 20x - 4{x^3} + 40{x^2} - 100x\\
= 44{x^3} - 11{x^2} - 200x - 154\\
d)\\
D = \left( { - 4x + 2y} \right)\left( { - 4x - 2y} \right)\\
+ {\left( {x - 5y} \right)^2} - {\left( {3x + 2y} \right)^2} - 7x\left( {x - 3y} \right)\\
= {\left( { - 4x} \right)^2} - {\left( {2y} \right)^2} + {x^2} - 10xy + 25{y^2}\\
- 9{x^2} - 12xy - 4{y^2} - 7{x^2} + 21xy\\
= {x^2} + 17{y^2} - xy
\end{array}$
