Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
*)\\
4{x^2} - 25 - \left( {2x - 5} \right)\left( {2x + 7} \right)\\
= \left( {4{x^2} - 25} \right) - \left( {2x - 5} \right)\left( {2x + 7} \right)\\
= \left[ {{{\left( {2x} \right)}^2} - {5^2}} \right] - \left( {2x - 5} \right)\left( {2x + 7} \right)\\
= \left( {2x - 5} \right)\left( {2x + 5} \right) - \left( {2x - 5} \right)\left( {2x + 7} \right)\\
= \left( {2x - 5} \right).\left[ {\left( {2x + 5} \right) - \left( {2x + 7} \right)} \right]\\
= \left( {2x - 5} \right).\left( { - 2} \right)\\
= - 2.\left( {2x - 5} \right)\\
*)\\
{x^3} + 27 + \left( {x + 3} \right)\left( {x - 9} \right)\\
= \left( {{x^3} + {3^3}} \right) + \left( {x + 3} \right)\left( {x - 9} \right)\\
= \left( {x + 3} \right)\left( {{x^2} - 3.x + {3^2}} \right) + \left( {x + 3} \right)\left( {x - 9} \right)\\
= \left( {x + 3} \right).\left[ {\left( {{x^2} - 3x + 9} \right) + \left( {x - 9} \right)} \right]\\
= \left( {x + 3} \right).\left( {{x^2} - 2x} \right)\\
= x.\left( {x + 3} \right)\left( {x - 2} \right)
\end{array}\)
Em xem lại đề câu đầu nhé!
