Chapter 8.3, Problem 10P

Simplify each product using a table.

$(x+3)(x-5)$

To determine

To find : the product of the given expression

Answer to Problem 10P

The product of the expression $\left(x+3\right)\left(x-5\right)$ is $\boxed{x^2-2x-15}$

Explanation of Solution

Given information : $\left(x+3\right)\left(x-5\right)$

Concept Involved:

Create a $2\times 2$ table whose sides represents each binomial. Find the area of each box by finding the product corresponding sides. Add all the box to find the expression that representing the area of whole table and equivalent to given expression

Calculation: Create a $2\times 2$ table whose sides represents each binomial

	$x$	$+3$
$x$
$-5$

Find the area of each box by finding the product corresponding sides

	$x$	$+3$
$x$	$x^2$	$+3x$
$-5$	$-5x$	$-15$

Add all the box to find the expression that representing the area of whole table

$x^2+3x-5x-15$

Combine like terms

$x^2-2x-15$

Conclusion:

The product of the expression $\left(x+3\right)\left(x-5\right)$ is $\boxed{x^2-2x-15}$