Đáp án:

$\begin{array}{l}
1)a){\left( {a + b + c} \right)^3}\\
 = {a^3} + 3{a^2}\left( {b + c} \right) + 3a{\left( {b + c} \right)^2} + {\left( {b + c} \right)^3}\\
 = {a^3} + 3\left( {b + c} \right)\left( {{a^2} + a\left( {b + c} \right)} \right) + {b^3} + 3{b^2}c + 3b{c^2} + {c^3}\\
 = {a^3} + {b^3} + {c^3} + 3\left( {b + c} \right)\left( {{a^2} + ab + ac} \right) + 3bc\left( {b + c} \right)\\
 = {a^3} + {b^3} + {c^3} + 3\left( {b + c} \right)\left( {{a^2} + ab + ac + bc} \right)\\
 = {a^3} + {b^3} + {c^3} + 3\left( {b + c} \right)\left( {a + b} \right)\left( {a + c} \right)\\
b){\left( {x + y} \right)^3} - {\left( {x - y} \right)^3}\\
 = {x^3} + 3{x^2}y + 3x{y^2} + {y^3}\\
 - \left( {{x^3} - 3{x^2}y + 3x{y^2} - {y^3}} \right)\\
 = 6{x^2}y + 2{y^3}\\
 = 2y\left( {{y^2} + 3{x^2}} \right)\\
B2)a){99^3}\\
 = {\left( {100 - 1} \right)^3}\\
 = {100^3} - {3.100^2} + 3.100 - 1\\
 = 1000000 - 30000 + 300 - 1\\
 = 970000 + 299\\
 = 970299\\
b){91^3} + {3.91^2}.9 + {3.91.9^2}\\
 = {91^3} + {3.91^2}.9 + {3.91.9^2} + {9^3} - {9^3}\\
 = {\left( {91 + 9} \right)^3} - 81.9\\
 = {100^3} - 729\\
 = 1000000 - 729\\
 = 999271\\
c){1001^3}\\
 = {\left( {1000 + 1} \right)^3}\\
 = {1000^3} + {3.1000^2} + 3.1000 + 1\\
 = 1000000000 + 3000000 + 3000 + 1\\
 = 1003003001\\
d){102^3} - {6.102^2} + 12.102 - 8\\
 = {\left( {102 - 2} \right)^3}\\
 = {100^3}\\
 = 1000000\\
B3)a)A = {x^3} - 3{x^2} + 3x - 1\\
 = {\left( {x - 1} \right)^3}\\
 = {\left( {1001 - 1} \right)^3}\\
 = {1000^3}\\
 = 1000000000\\
b)B = 8{x^3} + 12{x^2} + 6x + 1\\
 = {\left( {2x + 1} \right)^3}\\
 = {\left( {2.24,5 + 1} \right)^3}\\
 = {50^3}\\
 = 125000\\
c)C = \dfrac{{{x^3}}}{{27}} - 1 - \dfrac{{{x^2}}}{3} + x\\
 = \dfrac{{{x^3}}}{{27}} - \dfrac{{{x^2}}}{3} + x - 1\\
 = {\left( {\dfrac{x}{3} - 1} \right)^3}\\
 = {\left( {\dfrac{{303}}{3} - 1} \right)^3}\\
 = {\left( {101 - 1} \right)^3}\\
 = {100^3}\\
 = 1000000\\
d)D = {\left( {x + y} \right)^3} - 9{\left( {x + y} \right)^2} + 27\left( {x + y} \right) - 27\\
 = {\left( {x + y - 3} \right)^3}\\
 = {\left( {2 + 6 - 3} \right)^3}\\
 = {5^3}\\
 = 125
\end{array}$