Question

A rectangle has side lengths of x + 3 and 2 – x. Find an expression that describes the area of the rectangle.

Answer 1

D

Explanation:

distributive property:

2x - x^2 + 6 - 3x

simplify:

-x^2 - x + 6

Answer 2

D

Explanation:

We find the area of a rectangle by multiplying the lengths of both the sides (length and width).

• One side given is
  `x+3`
• Another side given is
  `2-x`

Multiplying these 2 will give us the expression for the area of the rectangle (we use distributive property given by
`a(b+c)=ab+ac` in this problem to multiply)

Area =
`(x+3)(2-x)\\=2x-x^2+6-3x`

Now combining like terms and rearranging, we have:

`2x-x^2+6-3x\\=-x-x^2+6\\=-x^2-x+6`

Answer choice D is right.