Answer
The expression for the product of two numbers $P$ which sums $66$ as a function of one of the numbers, $x$ is $P\left( x \right)=66x-{{x}^{2}}$.
Work Step by Step
Let the first number be x and the second number be $y$.
The sum of the number x and y is $66$.
$x+y=66$.
Rearrange for y.
$y=66-x$.
Consider the product of two numbers.
$P=xy$
Substitute $66-x$ for $y$.
$\begin{align}
& P=x\left( 66-x \right) \\
& p=66x-{{x}^{2}} \\
\end{align}$
The product is a function of x which can also be expressed as,
$P\left( x \right)=66x-{{x}^{2}}$
Hence, the expression for the product of two numbers $P$ which sums to $66$ as a function of one of the numbers, $x$ is $P\left( x \right)=66x-{{x}^{2}}$.
