Question

Write an expression for the area of the shaded region in its simplest form. Show all of your steps

Answer 1

"To solve this problem you will need to find the area of the shaded region (x+10)(2x+5) by FOIL Then you will need to find the area of the square (x+1)(x+1) by FOIL Finally, subtract the square from the rectangle to get the area of the shaded region."

Explanation:

Answer 2

A = lw - s²
A = (x + 10)(2x + 5) - (x + 1)²
A = (x(2x + 5) + 10(2x + 5)) - (x + 1)(x + 1)
A = (x(2x) + x(5) + 10(2x) + 10(5)) - (x(x + 1) + 1(x + 1))
A = (2x² + 5x + 20x + 50) - (x(x) + x(1) + 1(x) + 1(1))
A = (2x² + 25x + 50) - (x² + x + x + 1)
A = (2x² + 25x + 50) - (x² + 2x + 1)
A = (2x² - x²) + (25x - 2x) + (50 - 1)
A = x² + 23x + 49