Question

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

Answer 1

Answer:

$A=x^2+23x+49$

Step-by-step explanation:

Hi there!

The area of the shaded region is equal to the area of the big rectangle minus the area of the square.

Area of the big rectangle:

$A=lw\\A=(x+10)(2x+5)$

Area of the square:

$A=a^2\\A=(x+1)^2$

Area of the shaded region:

$A=(x+10)(2x+5)-(x+1)^2$

Expand:

$A=(x+10)(2x+5)-(x+1)^2\\A=2x^2+5x+20x+50-(x+1)^2\\A=2x^2+5x+20x+50-(x^2+2x+1)\\A=2x^2+5x+20x+50-x^2-2x-1$

Combine like terms:

$A=2x^2-x^2+5x+20x-2x+50-1\\A=x^2+23x+49$

I hope this helps!