Đáp án:
$\begin{array}{l}
(4):\\
a){\left( {3 + 1} \right)^3} = {3^3} + {3.3^2}.1 + {3.3.1^2} + {1^3}\\
= 27 + 27 + 9 + 1\\
= 64 = {4^3}\\
b){\left( {{x^2} + {y^2}} \right)^2}\\
= {\left( {{x^2}} \right)^3} + 3.{\left( {{x^2}} \right)^2}.{y^2} + 3.{x^2}.{\left( {{y^2}} \right)^2} + {\left( {{y^2}} \right)^3}\\
= {x^6} + 3{x^4}{y^2} + 3{x^2}{y^4} + {y^6}\\
c){\left( {2x + 3y} \right)^3}\\
= {\left( {2x} \right)^3} + 3.{\left( {2x} \right)^2}.3y + 3.2x.{\left( {3y} \right)^2} + {\left( {3y} \right)^3}\\
= 8{x^3} + 36{x^2}y + 54x{y^2} + 27{y^3}\\
(5)\\
a){99^3} = {\left( {100 - 1} \right)^3}\\
= {100^3} - {3.100^2}.1 + {3.100.1^2} - {1^3}\\
= 1000000 - 30000 + 300 - 1\\
= 970000 + 299\\
= 970299\\
b){\left( {\dfrac{1}{2}x - 3} \right)^3}\\
= {\left( {\dfrac{1}{2}x} \right)^3} - 3.{\left( {\dfrac{1}{2}x} \right)^2}.3 + 3.\dfrac{1}{2}x{.3^2} - {3^3}\\
= \dfrac{{{x^3}}}{8} - \dfrac{9}{4}{x^2} + \dfrac{{27}}{2}x - 27\\
c){8^3}\\
= {\left( {10 - 2} \right)^3}\\
= {10^3} - {3.10^2}.2 + {3.10.2^2} - {2^3}\\
= 1000 - 600 + 120 - 8\\
= 400 + 112\\
= 512
\end{array}$
