## Precalculus (6th Edition) Blitzer

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 $P\left( x \right)={{x}^{2}}-8x$.
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 ${{x}^{2}}+\left( -8 \right)x$