Question

Dylan uses the expressions (x^2 -2x+8) and (2x^2 + 5x - 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan’s room ?

Answer 1

c

Explanation:

Answer 2

`2x^4 + x^3 - x^2 +54x - 56` expression represents the area of Dylan’s room

Solution:

Given that,

Length of room =
`x^2 -2x+8`

Width of room =
`2x^2 + 5x - 7`

To find: Expression that the area (lw) of Dylan’s room

Since bedroom is generally of rectangular shape, we can use area of rectangle

The area of rectangle is given as:

`\text {area of rectangle }=\text { length } * \text { width }`

Substituting the given expressions of length and width,

`area = (x^2 -2x+8)(2x^2 + 5x - 7)`

We multiply each term inside first parenthesis with each term inside the second parenthesis.

So it becomes,

`2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56`

Now combine like terms,

`2x^4 + x^3 - x^2 +54x - 56`

Thus the above expression represents the area of Dylan’s room