Answer
The difference between the two numbers is 8. If one number is represented by x, the other number can be expresses as $8-x$. The product of the numbers, $P\left( x \right)$, expressed in the form $P\left( x \right)=a{{x}^{2}}+bx+c$, is $P\left( x \right)={{x}^{2}}-8x$.
Work Step by Step
The difference between the two number is 8. It is assumed that one number is x and the other number is y.
From the statement it is concluded that:
$\begin{align}
& x-y=8 \\
& -y=8-x \\
& y=x-8
\end{align}$
So, the other number is expressed as $8-x$.
$P\left( x \right)$ is the product of the numbers;
$\begin{align}
& P\left( x \right)=xy \\
& =x\left( x-8 \right) \\
& ={{x}^{2}}-8x
\end{align}$
So, the product of $P\left( x \right)$ is expressed in the form
$P\left( x \right)=a{{x}^{2}}+bx+c$ is ${{x}^{2}}+\left( -8 \right)x$
