a) A=(3x-1)^3-x(x^2+27)-(3x)^2 b)Cho ab=2 và a+b=5.Tính a^2 + b^2 và a^3 + b^3

Đáp án:

$\begin{array}{l}
a)A = {\left( {3x – 1} \right)^3} – x\left( {{x^2} + 27} \right) – {\left( {3x} \right)^2}\\
 = {\left( {3x} \right)^3} – 3.{\left( {3x} \right)^2}.1 + 3.3x.1 – 1 – {x^3} – 27x – 9{x^2}\\
 = 27{x^3} – 27{x^2} + 9x – 1 – {x^3} – 27x – 9{x^2}\\
 = 26{x^3} – 36{x^2} – 18x – 1\\
b)a.b = 2;a + b = 5\\
 + ){a^2} + {b^2}\\
 = {a^2} + 2ab + {b^2} – 2ab\\
 = {\left( {a + b} \right)^2} – 2ab\\
 = {5^2} – 2.2\\
 = 25 – 4 = 21\\
 + ){a^3} + {b^3}\\
 = {a^3} + 3{a^2}b + 3a{b^2} + {b^3} – 3{a^2}b – 3a{b^2}\\
 = {\left( {a + b} \right)^3} – 3ab\left( {a + b} \right)\\
 = {5^3} – 3.2.5\\
 = 125 – 30 = 95
\end{array}$