is this right

Question

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

Answer 1

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.