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}
$