Question

Suppose the height of a box is h feet. If the width of the box is two feet more than three times its height, then its width can be expressed as 2+3h.

If the length of the box is four feet less than two times its height, then its length can be expressed as 2h - 4.

The area of the base of the box is the product of its width and length. The area can be expressed as______which can be expanded to______.

Answer 1

A = 6h² - 8h - 8

Explanation:

given

width = 2 + 3h and length = 2h - 4

the area (A ) of the base is expressed as

A = width × length

= (2 + 3h)(2h - 4)

which can be expanded to

each term in the second factor is multiplied by each term in the first factor

2(2h - 4) + 3h(2h - 4) ← distribute parenthesis

= 4h - 8 + 6h² - 12h ← collect like terms

= 6h² - 8h - 8 ← in expanded form