contestada

Expand $\left(x^2 \frac{1}{x}\right)^3$. (Write the terms with higher degree first, so for example an $x^2$ term would come before $x$ or $\frac{1}{x}$.)

Respuesta :

presipao

Answer:

[tex]x^6+3x^3+3+\dfrac{1}{x^3}[/tex]

Step-by-step explanation:

We can use the pascal triangle to find the coefficients of the expasion of the cube. It holds that

[tex](x^2 + \dfrac{1}{x})^3=(x^2)^3+3(x^2)^2\dfrac{1}{x}+3x^2(\dfrac{1}{x})^2+(\dfrac{1}{x})^3\\\\=x^6+3x^4\dfrac{1}{x}+3x^2\dfrac{1}{x^2}+\dfrac{1}{x^3}\\\\=x^6+3x^3+3+\dfrac{1}{x^3}[/tex]