Answer:
x^2 +23x +49
Step-by-step explanation:
You know the area of a rectangle is given by the product of its length and width.
The area of the shaded region is the area of the larger rectangle with the area of the square white space subtracted.
The area of the larger rectangle is ...
large area = (length)(width) = (x+10)(2x+5)
Multiplying this out, we find the large area to be ...
large area = 2x^2 +5x +20x +50
large area = 2x^2 +25x +50
The area of the square can be found the same way:
square area = (x +1)(x +1) = x^2 +2x +1
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Then the shaded area is the difference of these:
shaded area = (large area) - (square area)
shaded area = (2x^2 +25x +50) - (x^2 +2x +1)
shaded area = 2x^2 +25x +50 -x^2 -2x -1 . . . . . . eliminate parentheses
shaded area = x^2 +23x +49 . . . . collect terms
