Let's start by looking at a rectangle with length 3x and width x + 1. I've broken the width into two chunks - the x chunk and the 1 chunk. If we look at the area of the two smaller rectangles, we can see that their areas are 3xx = 3x² and 3x(1) = 3x, making the total area so far 3x² + 3x. (Picture 1)
Now, to turn this rectangle into the one in the problem, we need to subtract 5 from the length. This has the effect of subtracting two smaller rectangles with areas 5x and 5 (picture 2), making our total area now 3x² + 3x - 5x - 5 (picture 3). Simplifying our expression, we find that the area of the rectangle in the problem is 3x² - 2x - 5 (picture 4)
