Bài 1. Ta có:
\(A = \left( {{m^3} - {n^3}} \right) - \left( {{m^3} + {n^3}} \right) = - 2{n^3}.\)
Bài 2. Ta có:
\(\left( {a - 1} \right)\left( {a - 2} \right)\left( {1 + a + {a^2}} \right)\left( {4 + 2a + {a^2}} \right)\)
\( = \left( {a - 1} \right)\left( {{a^2} + a + 1} \right)\left( {a - 2} \right)\left( {{a^2} + 2a + 4} \right)\)
\( = \left( {{a^3} - 1} \right)\left( {{a^3} - 8} \right) \)
\(= {a^6} - 8{a^3} - {a^3} + 8 \)
\(= {a^6} - 9{a^3} + 8\) (đpcm).
Bài 3. Ta có:
\(\left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right) - x\left( {x - 3} \right)\left( {x + 3} \right)\)
\( = {x^3} + 8 - x\left( {{x^2} - 9} \right) \)
\(= {x^3} + 8 - {x^3} + 9x = 9x + 8\)
Vậy \(9x + 8 = 26 \Rightarrow x = 2.\)
