Đáp án:
\(\begin{array}{l}
1)5xy\left( {xy + 4x - 7y} \right)\\
2)3{\left( {x - 2y} \right)^2}\\
3)xy\left( { - 3y + xy - 5x} \right)\\
4)x\left( {y - 1} \right) + 3{\left( {y + 1} \right)^2}\\
5)3x{\left( {2y - 1} \right)^2}\\
6)10\left( {x - y} \right){\left( {x + y} \right)^2}\\
7)\left( {4x - 5} \right)\left( { - 2x - 1} \right)\\
8)\left( {x + y + 2} \right)\left( {x + y - 2} \right)\\
9)\left( {2x - 1} \right)\left( { - {x^2} - x + 7} \right)
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)5xy\left( {xy + 4x - 7y} \right)\\
2)3x\left( {x - 2y} \right) - 6y\left( {x - 2y} \right)\\
= \left( {x - 2y} \right)\left( {3x - 6y} \right)\\
= 3{\left( {x - 2y} \right)^2}\\
3)xy\left( { - 3y + xy - 5x} \right)\\
4)x\left( {y - 1} \right) + 3{\left( {y + 1} \right)^2}\\
5)3x\left( {4{y^2} - 4y + 1} \right)\\
= 3x{\left( {2y - 1} \right)^2}\\
6)10{x^2}\left( {x + y} \right) - 5.2{y^2}\left( {x + y} \right)\\
= \left( {x + y} \right)\left( {10{x^2} - 10{y^2}} \right)\\
= 10\left( {x - y} \right){\left( {x + y} \right)^2}\\
7)\left( {x - 3 - 2 + 3x} \right)\left( {x - 3 + 2 - 3x} \right)\\
= \left( {4x - 5} \right)\left( { - 2x - 1} \right)\\
8){\left( {x + y} \right)^2} - 4\\
= \left( {x + y + 2} \right)\left( {x + y - 2} \right)\\
9)\left( {x + 1 + x - 2} \right)\left( {{x^2} + 2x + 1 - \left( {x + 1} \right)\left( {x - 2} \right) + {x^2} - 4x + 4} \right)\\
= \left( {2x - 1} \right)\left( { - 2x + 5 - {x^2} + x + 2} \right)\\
= \left( {2x - 1} \right)\left( { - {x^2} - x + 7} \right)
\end{array}\)
