Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
4,\\
a,\\
N = {\left( {x + 3} \right)^3} + {\left( {x - 3} \right)^3} - 2.\left( {x - 1} \right).\left( {{x^2} + x + 1} \right)\\
= \left( {{x^3} + 9{x^2} + 27x + 27} \right) + \left( {{x^3} - 9{x^2} + 27x - 27} \right) - 2.\left( {{x^3} - {1^3}} \right)\\
= \left( {2{x^3} + 54x} \right) - \left( {2{x^3} - 2} \right)\\
= 54x + 2\\
b,\\
N = 2020\\
\Leftrightarrow 54x + 2 = 2020\\
\Leftrightarrow 54x = 2018\\
\Leftrightarrow x = \frac{{1009}}{{27}}\\
3,\\
a,\\
M = {\left( {x + 3} \right)^2} + {\left( {x - 5} \right)^2} - 2x.\left( {x - 4} \right)\\
= \left( {{x^2} + 6x + 9} \right) + \left( {{x^2} - 10x + 25} \right) - \left( {2{x^2} - 8x} \right)\\
= \left( {2{x^2} - 4x + 34} \right) - 2{x^2} + 8x\\
= 4x + 34\\
b,\\
x = - \frac{1}{4} \Rightarrow M = 4.\left( { - \frac{1}{4}} \right) + 34 = 33\\
c,\\
M = 134\\
\Leftrightarrow 4x + 34 = 134\\
\Leftrightarrow 4x = 100\\
\Leftrightarrow x = 25
\end{array}\)
