Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
a,\\
M = \left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)\left( {x + 6} \right) + 9\\
= \left[ {\left( {x + 1} \right)\left( {x + 6} \right)} \right]\left[ {\left( {x + 3} \right)\left( {x + 4} \right)} \right] + 9\\
= \left( {{x^2} + 7x + 6} \right)\left( {{x^2} + 7x + 12} \right) + 9\\
= \left[ {\left( {{x^2} + 7x + 9} \right) - 3} \right]\left[ {\left( {{x^2} + 7x + 9} \right) + 3} \right] + 9\\
= {\left( {{x^2} + 7x + 9} \right)^2} - 9 + 9 = {\left( {{x^2} + 7x + 9} \right)^2}\\
b,\\
N = \left( {x - y} \right)\left( {x - 2y} \right)\left( {x - 3y} \right)\left( {x - 4y} \right) + {y^4}\\
= \left[ {\left( {x - y} \right)\left( {x - 4y} \right)} \right]\left[ {\left( {x - 2y} \right)\left( {x - 3y} \right)} \right] + {y^4}\\
= \left( {{x^2} - 5xy + 4{y^2}} \right)\left( {{x^2} - 5xy + 6{y^2}} \right) + {y^4}\\
= \left[ {\left( {{x^2} - 5xy + 5{y^2}} \right) - {y^2}} \right]\left[ {\left( {{x^2} - 5xy + 5{y^2}} \right) + {y^2}} \right] + {y^4}\\
= {\left( {{x^2} - 5xy + 5{y^2}} \right)^2} - {y^4} + {y^4}\\
= {\left( {{x^2} - 5xy + 5{y^2}} \right)^2}
\end{array}\]
