Đáp án:
$\begin{array}{l}
a)4{x^2} + 4x\_1\\
= {\left( {2x} \right)^2} + 2.2x + 1\\
= {\left( {2x + 1} \right)^2}\\
b){x^2} + 6x + 9\\
= {x^2} + 2.3x + {3^2}\\
= {\left( {x + 3} \right)^2}\\
c)9{x^2} - 6x + 1\\
= {\left( {3x} \right)^2} - 2.3x + 1\\
= {\left( {3x - 1} \right)^2}\\
d)4{x^2} - 25\\
= \left( {2x - 5} \right)\left( {2x + 5} \right)\\
e)27{x^3} + 1\\
= \left( {3x + 1} \right)\left( {9{x^2} - 3x + 1} \right)\\
f)8{x^3} - {y^3}\\
= \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)
\end{array}$
$\begin{array}{l}
g){\left( {2x + 1} \right)^2} - {\left( {2x - 1} \right)^2}\\
= \left( {2x + 1 - 2x + 1} \right)\left( {2x + 1 + 2x - 1} \right)\\
= 8x\\
h){\left( {a + b} \right)^3} - {\left( {a - b} \right)^3}\\
= \left( {a + b - a + b} \right)\left[ {{{\left( {a + b} \right)}^2} + \left( {a + b} \right)\left( {a - b} \right) + {{\left( {a - b} \right)}^2}} \right]\\
= 2b.\left( {{a^2} + 2ab + {b^2} + {a^2} - {b^2} + {a^2} - 2ab + {b^2}} \right)\\
= 2b.\left( {3{a^2} + {b^2}} \right)\\
i){\left( {x - 2} \right)^3} - {\left( {x + 2} \right)^3}\\
= \left( {x - 2 - x - 2} \right)\left[ {{{\left( {x - 2} \right)}^2} + \left( {x - 2} \right)\left( {x + 2} \right) + {{\left( {x + 2} \right)}^2}} \right]\\
= - 4\left( {{x^2} - 4x + 4 + {x^2} - 4 + {x^2} + 4x + 4} \right)\\
= - 4\left( {3{x^2} + 4} \right)\\
k)8{x^3} - 12{x^2}y + 6x{y^2} - {y^3}\\
= {\left( {2x} \right)^3} - 3.{\left( {2x} \right)^2}y + 3.2xy - {y^3}\\
= {\left( {2x - y} \right)^3}
\end{array}$
