Bài 1.
a) \({a^5} - {a^3} + {a^2} - 1 = \left( {{a^5} - {a^3}} \right) + \left( {{a^2} - 1} \right) \)
\(= {a^3}\left( {{a^2} - 1} \right) + \left( {{a^2} - 1} \right)\)
\( = \left( {{a^2} - 1} \right)\left( {{a^3} + 1} \right) \)
\(= \left( {a - 1} \right)\left( {a + 1} \right)\left( {a + 1} \right)\left( {{a^2} - a + 1} \right)\)
\( = \left( {a - 1} \right){\left( {a + 1} \right)^2}\left( {{a^2} - a + 1} \right).\)
b) \(48x{z^2} + 32x{y^2} - 15y{z^2} - 10{y^3} \)
\(= \left( {58x{z^2} + 32x{y^2}} \right) + \left( { - 15y{z^2} - 10{y^3}} \right)\)
\( = 16\left( {3{z^2} + 2{y^2}} \right) - 5y\left( {3{z^2} + 2{y^2}} \right) \)
\(= \left( {3{z^2} + 2{y^2}} \right)\left( {16x - 5y} \right).\)
c) \(a{x^2} - ay - b{x^2} + cy + by - c{x^2} \)
\(= \left( {a{x^2} - b{x^2} - c{x^2}} \right) + \left( { - ay + cy + by} \right)\)
\( = {x^2}\left( {a - b - c} \right) - y\left( {a - b - c} \right)\)
\( = \left( {a - b - c} \right)\left( {{x^2} - y} \right)\)
Bài 2.
\(2x\left( {3x - 5} \right) = 10 - 6x\)
\( \Rightarrow 2x\left( {3x - 5} \right) + 2\left( {3x - 5} \right) = 0 \)
\(\Rightarrow \left( {3x - 5} \right)\left( {2x + 2} \right) = 0\)
\( \Rightarrow 3x - 5 = 0\) hoặc \(2x + 2 = 0\)
\(\Rightarrow x = {5 \over 3}\) hoặc \(x = - 1\) .
