Question

Find the area of the shaded region.

Answer 1

Hello!

You first have to find the area of the bigger rectangle

You find this by multiplying the sides

(x + 1)(x + 1) = x^2 + 2x + 1

Next you have to find the area of the smaller rectangle

(x - 7) * 5 = 5x - 35

Subtract the two polynomials

(x^2 + 2x + 1) - (5x - 35) = x^2 - 3x + 36

The answer is $x^{2} -3x + 36$

Hope this helps!

Answer 2

1)
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1

2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35

3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36

area of the shaded region = x^2 - 3x + 36