Bài 78. Rút gọn các biểu thức sau :
a) \(\left( {x + 2} \right)\left( {x - 2} \right) - \left( {x - 3} \right)\left( {x + 1} \right)\) ;
b) \({\left( {2x + 1} \right)^2} + {\left( {3x - 1} \right)^2} + 2\left( {2x + 1} \right)\left( {3x - 1} \right)\) .
Giải  
a) \(\left( {x + 2} \right)\left( {x - 2} \right) - \left( {x - 3} \right)\left( {x + 1} \right) \)
=\( {x^2} - {2^2} - \left( {{x^2} + x - 3x - 3} \right)\)
=\({x^2} - 4 - {x^2} - x + 3x + 3\)
=\(2x-1\)  ;
b) \({\left( {2x + 1} \right)^2} + {\left( {3x - 1} \right)^2} + 2\left( {2x + 1} \right)\left( {3x - 1} \right)\)
=\({\left( {2x + 1} \right)^2} + 2.\left( {2x + 1} \right)\left( {3x - 1} \right) + {\left( {3x - 1} \right)^2}\)
=\({\left[ {\left( {2x + 1} \right) + \left( {3x - 1} \right)} \right]^2}\)
= \({\left( {2x + 1 + 3x - 1} \right)^2}\)
=\({\left( {5x} \right)^2} = 25{x^2}\)