is this right
First we find the area of the rectangle as though the small square were not cut out of it
A = (x+10) (2x+5)
Foil
2x^2 +5x+20x+50
2x^2 +25x+50
Then we find the area of the small square
A = (x+1) (x+1)
FOIL
x^2 +x+x+1
x^2 +2x+1
Then we subtract the small square from the large rectangle to find the area of the shaded region
2x^2 +25x+50 - (x^2 +2x+1)
Distribute the minus sign
2x^2 +25x+50 - x^2 -2x-1
x^2 +23x +49
There are a couple of arithmetic errors in your calculations.
First, when finding the area of the large rectangle, the correct foil calculation should be:
A = (x+10)(2x+5) = 2x^2 + 5x + 20x + 50 = 2x^2 + 25x + 50
Then, when finding the area of the small square, the correct foil calculation should be:
A = (x+1)(x+1) = x^2 + x + x + 1 = x^2 + 2x + 1
Finally, when subtracting the area of the small square from the large rectangle, the correct calculation should be:
2x^2 + 25x + 50 - (x^2 + 2x + 1) = 2x^2 + 25x + 50 - x^2 - 2x - 1 = x^2 + 23x + 49
So the corrected answer for the area of the shaded region is x^2 + 23x + 49.