Find the area of the shaded region. show all your work.

The teachers this is commonly known as a doughnut problem. Basically you find the area of the large trays and subtract the area of the small shape.

Lg. Rectangle. Sm. Rectangle
A = lw. A=lw
A=(3x - 4)(2x + 2) A=(x - 3)(x - 6). Use FOIL on each
A = 6x^2 + 6x - 8x -8 A=x^2 - 6x - 3x + 18. Combine like terms
A = 6x^2 - 2x - 8. A=x^2 - 9x + 18. Subtract rectangles to find area of shaded region
A = 6x^2 -2x - 8 - (x^2 - 9x + 18) Distribute the negative into the parenthesis (multiply each term by -1)
A = 6x^2 - 2x - 8 - x^2 + 9x -18. Combine like terms
A = 5x^2 + 7x - 26. <— answer