Question

Help me please! LAST TWO QUESTIONS.

Answer 1

1)
`(4x)(x+2)-x(3x+5)`

2A)
`w^2+3w`

2B)
`28\text{ in}^2`

Explanation:

1)

First, let's write the expressions for the area of the entire shaded region and the white area.

The formula for the area of a rectangle is given by:

`A=lw`

For the entire shaded rectangle, the length is (4x) and the width is (x+2). So, the area is:

`(4x)(x+2)`

For the white rectangle, the length is (3x+5) and the width is (x). So, the area is:

`x(3x+5)`

The shaded area is the entire shaded rectangle minus the area of the white rectangle. Therefore, our expression would be:

`(4x)(x+2)-x(3x+5)`

2)

Part A)

So, we are given that the length of the rectangle is 3 inches greater than the width.

The area of a rectangle is given by:

`A=lw`

So, let w be width and let l be the length.

Since the length is 3 inches greater than the width, this means that the l is (w+3).

Thus, substitute. Our expression will therefore be:

`lw\\w(w+3)`

Since we want a polynomial, let's expand:

`=w^2+3w`

Part B)

To find the area when the width is 4, substitute 4 for w:

`w^2+3w\\=(4)^2+3(4)`

Square and multiply:

`=16+12`

Add:

`=28\text{ in}^2`

So the area is 28 square inches.