Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{\left( {x + 1} \right)^4}.{\left( {x + 3} \right)^4}.{\left( {x + 5} \right)^4}\\
= {\left[ {\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 5} \right)} \right]^4}\\
b,\\
\left( {x + 1} \right).{\left( {x + 1} \right)^2}{\left( {x + 1} \right)^3}........{\left( {x + 1} \right)^{99}}.{\left( {x + 1} \right)^{100}}\\
= {\left( {x + 1} \right)^{1 + 2 + 3 + .... + 99 + 100}}\\
= {\left( {x + 1} \right)^{\frac{{\left( {1 + 100} \right).100}}{2}}} = {\left( {x + 1} \right)^{5050}}\\
2,\\
{50^{n + 1}} - {50^n} + {125000^{\frac{1}{3}\left( {n + 1} \right)}}\\
= {50.50^n} - {50^n} + {\left( {{{50}^3}} \right)^{\frac{1}{3}\left( {n + 1} \right)}}\\
= {50.50^n} - {50^n} + {50^{n + 1}}\\
= {50^n}\left( {50 - 1 + 50} \right)\\
= {50^n}.99 \vdots 11
\end{array}\)
