Question

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 $\frac{1}{x}$.)

Answer 1

Answer:

$x^6+3x^3+3+\dfrac{1}{x^3}$

Step-by-step explanation:

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

$(x^2 + \dfrac{1}{x})^3=(x^2)^3+3(x^2)^2\dfrac{1}{x}+3x^2(\dfrac{1}{x})^2+(\dfrac{1}{x})^3\\\\=x^6+3x^4\dfrac{1}{x}+3x^2\dfrac{1}{x^2}+\dfrac{1}{x^3}\\\\=x^6+3x^3+3+\dfrac{1}{x^3}$