Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 94

Translate the phrase "the sum of five more than the square of a number and twice the square of the number" into a variable expression. Then simplify the expression.

$\begin{equation} \begin{aligned} & \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\ \\ & \text{Square of the number: } n^2 && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\ \\ & \text{Twice the square of the number: } 2n^2 \\ \\ & \text{Five more than the square of the number: } n^2 + 5\\ \\ &= (n^2 + 5) + (2n^2) && \text{Use the assigned variable to write the variable expression.}\\ \\ &= 2n^2 + n^2 + 5&& \text{Use the Commutative Property of Addition}\\ \\ &= 3n^2 + 5 && \text{Simplify} \end{aligned} \end{equation}$