Respuesta :

Answer:

x²+23x+49

Step-by-step explanation:

The area of the large rectangle can be found by multiplying the dimensions, x+10 and 2x+5:

(x+10)(2x+5)

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

2x²+5x+20x+50

2x²+25x+50

Next find the area of the smaller rectangle.  Do this by multiplying x+1 by x+1:

(x+1)(x+1)

x(x)+1(x)+1(x)+1(1)

x²+1x+1x+1

x²+2x+1

Now subtract the larger area and the smaller area:

(2x²+25x+50)-(x²+2x+1)

To do this, combine like terms:

2x²-x²+25x-2x+50-1

x²+23x+49

adioabiola

An expression for the area of the shaded part is; x²+23x-49

Area of shaded part

The area of the unshaded small square is;

  • (x+1)×(x+1)

  • A(square) = x² +2x+1

Area of the large rectangle = (2x+5)(x+10)

  • Hence, A(rectangle) = 2x²+25x+50

Hence, Area of the shaded region;

  • A(shaded) = 2x²+ 25x +50 - x² - 2x -1

  • A(shaded) = x² +23x -49

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