a) Tìm đa thức A trong đẳng thức: x^2+ 2xy+ y^2/ x-y = A/x^2-y^2

* Hướng dẫn giải

$$\begin{gathered} \mathrm{a}) \frac{{\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2}{\mathrm{x}-\mathrm{y}}=\frac{\mathrm{A}}{{\mathrm{x}}^2-{\mathrm{y}}^2}\Rightarrow \frac{{(\mathrm{x}+\mathrm{y})}^2}{\mathrm{x}-\mathrm{y}}=\frac{\mathrm{A}}{{\mathrm{x}}^2-{\mathrm{y}}^2} \\ \Rightarrow \frac{{(\mathrm{x}+\mathrm{y})}^2(\mathrm{x}+\mathrm{y})}{(\mathrm{x}-\mathrm{y})(\mathrm{x}+\mathrm{y})}=\frac{\mathrm{A}}{{\mathrm{x}}^2-{\mathrm{y}}^2}\Rightarrow \frac{{(\mathrm{x}+\mathrm{y})}^3}{{\mathrm{x}}^2-{\mathrm{y}}^2}=\frac{\mathrm{A}}{{\mathrm{x}}^2-{\mathrm{y}}^2} \\ \mathrm{Vậy} \mathrm{A}={(\mathrm{x}+\mathrm{y})}^3={\mathrm{x}}^3+3{\mathrm{x}}^2\mathrm{y}+3{\mathrm{xy}}^2+{\mathrm{y}}^3 \end{gathered}$$