Đáp án:
\(\begin{array}{l}
b,\,\,\,\, - 1\\
c,\,\,\,\,\,2
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
b,\\
2\left( {{x^3} + {y^3}} \right) - 3\left( {{x^2} + {y^2}} \right)\\
= 2.\left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right) - 3.\left( {{x^2} + {y^2}} \right)\\
= 2.1.\left( {{x^2} - xy + {y^2}} \right) - 3.\left( {{x^2} + {y^2}} \right)\\
= \left( {2{x^2} - 2xy + 2{y^2}} \right) - \left( {3{x^2} + 3{y^2}} \right)\\
= 2{x^2} - 2xy + 2{y^2} - 3{x^2} - 3{y^2}\\
= - {x^2} - 2xy - {y^2}\\
= - \left( {{x^2} + 2xy + {y^2}} \right)\\
= - {\left( {x + y} \right)^2}\\
= - {1^2}\\
= - 1\\
c,\\
\dfrac{{{{\left( {x + 5} \right)}^2} + {{\left( {x - 5} \right)}^2}}}{{{x^2} + 25}}\\
= \dfrac{{\left( {{x^2} + 2.x.5 + {5^2}} \right) + \left( {{x^2} - 2.x.5 + {5^2}} \right)}}{{{x^2} + 25}}\\
= \dfrac{{\left( {{x^2} + 10x + 25} \right) + \left( {{x^2} - 10x + 25} \right)}}{{{x^2} + 25}}\\
= \dfrac{{2{x^2} + 50}}{{{x^2} + 25}}\\
= \dfrac{{2.\left( {{x^2} + 25} \right)}}{{{x^2} + 25}}\\
= 2
\end{array}\)
