Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
2,\\
- 12{x^3} + 75x{y^3} = - 3x\left( {4{x^2} - 25{y^3}} \right)\\
3,\\
9xy - 4{a^2}xy = - xy\left( {4{a^2} - 9} \right) = - xy\left( {2a - 3} \right)\left( {2a + 3} \right)\\
4,\\
8{a^3}x - 27{b^3}x = x.\left( {8{a^3} - 27{b^3}} \right)\\
= x.\left[ {{{\left( {2a} \right)}^3} - {{\left( {3b} \right)}^3}} \right]\\
= x.\left( {2a - 3b} \right).\left( {4{a^2} + 6ab + 9{b^2}} \right)\\
5,\\
- 4 + 32{a^3}{b^3} = 4.\left( {8{a^3}{b^3} - 1} \right)\\
= 4.\left( {2ab - 1} \right).\left( {4{a^2}{b^2} + 2ab + 1} \right)\\
6,\\
10{a^3} - 10a = 10a.\left( {{a^2} - 1} \right) = 10a.\left( {a - 1} \right)\left( {a + 1} \right)\\
7,\\
8{a^2}xy - 18{b^2}xy = 2xy\left( {4{a^2} - 9{b^2}} \right) = 2xy\left( {2a - 3b} \right)\left( {2a + 3b} \right)\\
8,\\
2x{m^3} - 2x = 2x\left( {{m^3} - 1} \right) = 2x.\left( {m - 1} \right)\left( {{m^2} + m + 1} \right)\\
9,\\
16{a^3}xy - 54{b^3}x{y^4}\\
= 2xy\left( {8{a^3} - 27{b^3}{y^3}} \right)\\
= 2xy\left( {2a - 3by} \right).\left( {4{a^2} + 2a.3by + 9{b^2}{y^2}} \right)\\
= 2xy\left( {2a - 3by} \right).\left( {4{a^2} + 6aby + 9{b^2}{y^2}} \right)\\
10,\\
5xy - 40{a^3}{b^3}xy\\
= 5xy\left( {1 - 8{a^3}{b^3}} \right)\\
= 5xy\left( {1 - 2ab} \right)\left( {1 + 2ab + 4{a^2}{b^2}} \right)
\end{array}\)
