Respuesta :

Answer: x^2 + 23x + 49

Step-by-step explanation:

The area of the shaded region is the area of the big rectangle minus the square

area of rectangle

area = bh

b = 2x + 5

h = x + 10

area = (2x+5)(x+10) FOIL

= 2x^2 + 20x + 5x + 50

= 2x^2 + 25x + 50

area of square

area = s * s

s = x + 1

area = (x+1)(x+1) FOIL

= x^2 + x + x + 1

= x^2 + 2x + 1

area of shaded region

now subtract rectangle - square

(2x^2 + 25x + 50) - (x^2 + 2x + 1)

= 2x^2 + 25x + 50 - x^2 - 2x - 1 combine like terms

= x^2 + 23x + 49

Answer:

(x² + 23x + 49) units²

Step-by-step explanation:

(x + 10)(2x + 5) - (x + 1)²

(2x² + 20x + 5x + 50) - (x² + 2x + 1)

2x² + 25x + 50 - x² - 2x - 1

x² + 23x + 49

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