Question

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

Answer 1

The area of the shaded region in its simplest form is:

• 
  `x^2+23x+49`

Explanation:

The area of the shaded region can be calculated by subtracting the area of the small white square from the area of the large rectangle.

The area of a rectangle is the product of its width and length.

`\begin{aligned}\implies \textsf{Area of shaded region}&=(x+10)(2x+5)-(x+1)(x+1)\\&=(2x^2+5x+20x+50)-(x^2+x+x+1)\\&=(2x^2+25x+50)-(x^2+2x+1)\\&=2x^2+25x+50-x^2-2x-1\\&=2x^2-x^2+25x-2x+50-1\\&=x^2+23x+49\end{aligned}`

Therefore, the area of the shaded region in its simplest form is:

• 
  `x^2+23x+49`