Question

You have asked a friend of yours who works in construction to help you determine the price of having a deck built. The only requirement you gave

him is that you want the length of the deck to be 8 feet greater than the width of the deck. Your friend gave you this expression to determine the
total cost of having the deck constructed based on the width, w, of the deck:
$58(w)(w + 8). (answer this as well)

Part A
How many factors are in this expression? Describe what each factor in the expression most likely represents.

Part B
expand the expression; does the expanded form give as much information as the given form?​

Answer 1

Answer: The expanded form is $58w^2 + $464w.

Explanation:

Part A:

The expression given to determine the total cost of having the deck constructed is $58(w)(w + 8).

There are three factors in this expression:

1. $58: This factor most likely represents the cost per square foot or the cost per unit of width.

2. (w): This factor represents the width of the deck.

3. (w + 8): This factor represents the length of the deck, which is 8 feet greater than the width.

Part B:

To expand the expression, we can use the distributive property:

$58(w)(w + 8) = $58(w^2 + 8w)

Expanding further, we get:

$58(w^2) + $58(8w) = $58w^2 + $464w

The expanded form, $58w^2 + $464w, gives us more information about the expression. It shows us the cost in terms of the width and width squared. Additionally, it provides the coefficient for each term, which represents the cost per unit of width and the cost of the 8-foot length increment.

In summary, the expression $58(w)(w + 8) has three factors representing the cost, width, and length of the deck. The expanded form, $58w^2 + $464w, provides more detailed information and shows the cost in terms of the width and width squared.