Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 52

Translate the phrase "a number decreased by the difference between the cube of the number and ten" into a variable expression.

$\begin{equation} \begin{aligned} & \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\ \\ & \text{Cube of the numerator: } n^3 && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\ \\ & \text{Difference between the cube of the number and ten: } n^3 - 10 && \text{Again, by using the assigned variable to write an expression for any other unknown quantity.}\\ \\ &= n - (n^3 - 10) && \text{Use the assigned variable to write the variable expression.}\\ \\ &= n - n^3 + 10 \end{aligned} \end{equation}$