Rút gọn các biểu thức sau: (a) 5x(5−x)+(x+1)(5x−3).

a) \[\,\,\,\,5x\left( {5 - x} \right) + \left( {x + 1} \right)\left( {5x - 3} \right)\]

\[ = 25x - 5{x^2} + 5{x^2} - 3x + 5x - 3\]

\[ = 27x - 3.\]

b) \[\,\,\,{\left( {2x + 3} \right)^2} - \left( {2x - 1} \right)\left( {2x + 1} \right)\]

\[ = 4{x^2} + 12x + 9 - \left[ {{{(2x)}^2} - 1} \right]\]

\[ = 4{x^2} + 12x + 9 - 4{x^2} + 1\]

\[ = 12x + 10.\]