Đáp án:
$\begin{array}{l}
3)a){x^2} - 100 = {x^2} - {10^2} = \left( {x - 10} \right)\left( {x + 10} \right)\\
b)9{x^2} - 18x + 9 = {\left( {3x} \right)^2} - 2.3.3.x + {3^2} = {\left( {3x - 3} \right)^2}\\
c){x^3} - 8 = \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)\\
e){x^2} + 6x{y^2} + 9{y^4} = {\left( {x + 3{y^2}} \right)^2}\\
f){x^6} - {y^6} = {\left( {{x^3}} \right)^2} - {\left( {{y^3}} \right)^2} = \left( {{x^3} - {y^3}} \right)\left( {{x^3} + {y^3}} \right)\\
g){\left( {x - 3} \right)^2} - {\left( {2 - 3x} \right)^2}\\
= \left( {x - 3 - 2 + 3x} \right)\left( {x - 3 + 2 - 3x} \right) = \left( {4x - 5} \right)\left( { - 1 - 2x} \right)\\
h){x^3} - 3{x^2} + 3x - 1 = {\left( {x - 1} \right)^3}\\
4)a)12x - 36{x^2} - 1 = - 36{x^2} + 12x - 1\\
= - {\left( {6x - 1} \right)^2}\\
b)4xy - 4{x^2} - {y^2} = - 4{x^2} + 4xy - {y^2}\\
= - {\left( {2x - y} \right)^2}\\
c)49{m^2} - 25{a^2} = \left( {7m - 5a} \right)\left( {7m + 5a} \right)\\
d){\left( {x + 4} \right)^2} - {\left( {y - 3} \right)^2}\\
= \left( {x + 4 - y + 3} \right)\left( {x + 4 + y - 3} \right) = \left( {x - y + 7} \right)\left( {x + y + 1} \right)\\
e) - {x^3} + 3{x^2} - 3x + 1 = 1 - 3x + 3{x^2} - {x^3}\\
= {\left( {1 - x} \right)^3}\\
g){y^3} + \dfrac{8}{{27}} = \left( {y + \dfrac{2}{3}} \right)\left( {{y^2} - \dfrac{2}{3}y + \dfrac{4}{9}} \right)\\
h)27{x^3} - 27{x^2}y + 9x{y^2} - {y^3}\\
= {\left( {3x - y} \right)^3}\\
i){\left( {x + y} \right)^2} - \left( {{x^2} - {y^2}} \right)\\
= {x^2} + 2xy + {y^2} - {x^2} + {y^2}\\
= 2xy + 2{y^2}\\
= 2x\left( {x + y} \right)
\end{array}$
