Mathematics: i need to write an expression for the shaded region in its simplest form, showing all of my steps! but it s late at night and i m not entirely sure how to do this, so you so much in !

i need to write an expression for the shaded region

david1236544

16.01.2022

x² + 23x + 49

Step-by-step explanation:

Area of the big rectangle

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

= 2x² + 5x + 20x + 50

= 2x² + 25x + 50

Area of the small white rectangle

= (x + 1)(x + 1)

= x² + x + x + 1

= x² + 2x + 1

Area of the shaded area

= (2x² + 25x + 50) - (x² + 2x + 1)

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49

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