Question

Write an expression for the area of the shaded region in it's simplest form.

Answer 1

We first need to find the area of the big rectangle, and then find the area of the smaller square.

If we do:
Area of big rectangle - Area of square = Area of shaded region.

(x+10)(2x+5) - (x+1)(x+1) = Area of shaded region

$\sf{Area = (x+10)(2x+5) - (x+1)(x+1)}\\\\\sf{Area = (2x^2+20x+5x+50) - (x+1)(x+1)}\\\\\sf{Area = (2x^2+25x+50) - (x+1)(x+1)}\\\\\sf{Area = (2x^2+25x+50) - (x^2 + x +x +1)}\\\\\sf{Area = (2x^2+25x+50) - (x^2 +2x +1)}\\\\\sf{Area = 2x^2+25x+50 - x^2 -2x -1}\\\\\sf{Area = 2x^2-x^2+25x-2x+50-1}\\\\\sf{\boxed{\bf{Area=x^2+23x-49}}}$