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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) \({\left( {2x + 1} \right)^2} + {\left( {3x – 1} \right)^2} + 2\left( {2x + 1} \right)\left( {3x – 1} \right)\) .
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) \({\left( {2x + 1} \right)^2} + {\left( {3x – 1} \right)^2} + 2\left( {2x + 1} \right)\left( {3x – 1} \right)\)
=\({\left( {2x + 1} \right)^2} + 2.\left( {2x + 1} \right)\left( {3x – 1} \right) + {\left( {3x – 1} \right)^2}\)
=\({\left[ {\left( {2x + 1} \right) + \left( {3x – 1} \right)} \right]^2}\)
= \({\left( {2x + 1 + 3x – 1} \right)^2}\)
=\({\left( {5x} \right)^2} = 25{x^2}\)