Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

Answer 1

Answer:

• x² + 23x + 49

Step-by-step explanation:

The shaded area is the difference of areas of the rectangle and the square.

Rectangle:

• A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Square:

• A₂ = (x + 1)² = x² + 2x + 1

Shaded region:

• A₁ - A₂ =
• 2x² + 25x + 50 - (x² + 2x + 1) =
• 2x² + 25x + 50 - x² - 2x - 1 =
• x² + 23x + 49

Answer 2

Answer:

area of shaded region: x² + 23x + 49

                                                solve:

Area of full rectangle:

$Length * Width$

$(x + 10 ) *( 2x + 5)$

$2x^2 + 5x + 20x + 50$

$2x^2 + 25x + 50$

Area of un-shaded rectangle:

$Length * Width$

$(x+1)(x+1)$

$x^2 + x+ x+ 1$

$x^2 + 2x + 1$

Area of shaded =  Area of full rectangle - Area of un-shaded rectangle

$\hookrightarrow 2x^2 + 25x + 50 - (x^2 + 2x + 1)$

$\hookrightarrow 2x^2 + 25x + 50 - x^2 - 2x - 1$

$\hookrightarrow x^2 + 23x +49$