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

`x^6+3x^3+3+(1)/(x^3)`

Explanation:

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

`(x^2 + (1)/(x))^3=(x^2)^3+3(x^2)^2(1)/(x)+3x^2((1)/(x))^2+((1)/(x))^3\\\\=x^6+3x^4(1)/(x)+3x^2(1)/(x^2)+(1)/(x^3)\\\\=x^6+3x^3+3+(1)/(x^3)`