Question

Help me please! These are due today.

Answer 1

`{x}^(2) + 3x`

Explanation:

1.

Area of shaded region = Area of external rectangle - Area of internal rectangle

`= 4x(x + 2) - x(3x + 5) \\ = 4 {x}^(2) + 8x - 3 {x}^(2) - 5x \\ = 4 {x}^(2) - 3 {x}^(2) + 8x - 5x \\ = {x}^(2) + 3x \\`

2.

Let the width of the rectangle be x inches.

Therefore, length of the rectangle = (x + 3) inches

A.

Area of rectangle

`=(x + 3)* x\\</p><p>=x^2 + 3x\\`

B.

Width of rectangle = 4 inches

Length of rectangle = 4 + 3 = 7 inches

Area of rectangle = 7*4 = 28 square inches.