Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
{x^3} + 2{x^2} + x\\
= x.\left( {{x^2} + 2x + 1} \right)\\
= x.{\left( {x + 1} \right)^2}\\
b,\\
{x^3} + 2{x^2}y + x{y^2} - 9x\\
= x\left( {{x^2} + 2xy + {y^2} - 9} \right)\\
= x.\left[ {{{\left( {x + y} \right)}^2} - {3^2}} \right]\\
= x.\left( {x + y - 3} \right)\left( {x + y + 3} \right)\\
c,\\
{x^2} - x - 20\\
= \left( {{x^2} - 5x} \right) + \left( {4x - 20} \right)\\
= x.\left( {x - 5} \right) + 4.\left( {x - 5} \right)\\
= \left( {x - 5} \right)\left( {x + 4} \right)\\
d,\\
{x^4} + 64\\
= \left( {{x^4} + 16{x^2} + 64} \right) - 16{x^2}\\
= {\left( {{x^2} + 8} \right)^2} - {\left( {4x} \right)^2}\\
= \left( {{x^2} + 8 - 4x} \right)\left( {{x^2} + 8 + 4x} \right)
\end{array}\)
