Đáp án:
\(\begin{array}{l}
6,\\
4\left( {2y - 17} \right)\left( {5y - 11} \right)\\
7,\\
\left( {y + z} \right).\left( {z - x} \right).\left( {y + x} \right)\\
8,\\
9{x^2}\left( {y - 2} \right).\left( {1 - 3x} \right)\left( {1 + 3x} \right)\\
9,\\
4x\left( {5 - 2y} \right)\\
10,\\
5.\left( {6x - 1} \right)
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
6,\\
49{\left( {y - 4} \right)^2} - 9{y^2} - 36y - 36\\
= {7^2}.{\left( {y - 4} \right)^2} - \left( {9{y^2} + 36y + 36} \right)\\
= {\left[ {7.\left( {y - 4} \right)} \right]^2} - \left[ {{{\left( {3y} \right)}^2} + 2.3y.6 + {6^2}} \right]\\
= {\left( {7y - 28} \right)^2} - {\left( {3y + 6} \right)^2}\\
= \left[ {\left( {7y - 28} \right) - \left( {3y + 6} \right)} \right].\left[ {\left( {7y - 28} \right) + \left( {3y + 6} \right)} \right]\\
= \left( {7y - 28 - 3y - 6} \right).\left( {7y - 28 + 3y + 6} \right)\\
= \left( {4y - 34} \right).\left( {10y - 22} \right)\\
= 2.\left( {2y - 17} \right).2.\left( {5y - 11} \right)\\
= 4\left( {2y - 17} \right)\left( {5y - 11} \right)\\
7,\\
yz\left( {y + z} \right) + xz\left( {z - x} \right) - xy\left( {x + y} \right)\\
= yz\left( {y + z} \right) + x{z^2} - {x^2}z - {x^2}y - x{y^2}\\
= yz\left( {y + z} \right) + \left( {x{z^2} - x{y^2}} \right) - \left( {{x^2}z + {x^2}y} \right)\\
= yz\left( {y + z} \right) + x.\left( {{z^2} - {y^2}} \right) - {x^2}\left( {z + y} \right)\\
= yz\left( {y + z} \right) - x.\left( {{y^2} - {z^2}} \right) - {x^2}\left( {y + z} \right)\\
= yz\left( {y + z} \right) - x.\left( {y - z} \right)\left( {y + z} \right) - {x^2}\left( {y + z} \right)\\
= \left( {y + z} \right).\left[ {yz - x.\left( {y - z} \right) - {x^2}} \right]\\
= \left( {y + z} \right).\left( {yz - xy + xz - {x^2}} \right)\\
= \left( {y + z} \right).\left[ {y\left( {z - x} \right) + x.\left( {z - x} \right)} \right]\\
= \left( {y + z} \right).\left( {z - x} \right).\left( {y + x} \right)\\
8,\\
9{x^2}\left( {y - 2} \right) - 81{x^4}\left( {y - 2} \right)\\
= \left( {y - 2} \right).\left( {9{x^2} - 81{x^4}} \right)\\
= \left( {y - 2} \right).9{x^2}.\left( {1 - 9{x^2}} \right)\\
= \left( {y - 2} \right).9{x^2}.\left[ {{1^2} - {{\left( {3x} \right)}^2}} \right]\\
= 9{x^2}\left( {y - 2} \right).\left( {1 - 3x} \right)\left( {1 + 3x} \right)\\
9,\\
{\left( {x + 5 - 4y} \right)^2} - {\left( {x + 4y - 5} \right)^2}\\
= \left[ {\left( {x + 5 - 4y} \right) + \left( {x + 4y - 5} \right)} \right].\left[ {\left( {x + 5 - 4y} \right) - \left( {x + 4y - 5} \right)} \right]\\
= \left[ {x + 5 - 4y + x + 4y - 5} \right].\left[ {x + 5 - 4y - x - 4y + 5} \right]\\
= 2x.\left( {10 - 4y} \right)\\
= 2x.2.\left( {5 - 2y} \right)\\
= 4x\left( {5 - 2y} \right)\\
10,\\
25{x^2} + 10x - 1 - {\left( {5x - 2} \right)^2}\\
= 25{x^2} + 10x - 1 - \left[ {{{\left( {5x} \right)}^2} - 2.5x.2 + {2^2}} \right]\\
= 25{x^2} + 10x - 1 - \left( {25{x^2} - 20x + 4} \right)\\
= 25{x^2} + 10x - 1 - 25{x^2} + 20x - 4\\
= 30x - 5\\
= 5.\left( {6x - 1} \right)
\end{array}\)
