Find an expression for the area of the shaded region in the figure below.
The area of the shaded region will be equal to the area of the large rectangle minus the area of the square that’s cut out. First, let’s write an expression for the area of the large rectangle. We find the area of rectangles by multiplying length times width; the length here is 13𝑥 and the width is six 𝑥.
Moving on to the area of the square, we find the area of a square by taking the side and multiplying it by itself or we say side squared. This square has a side length of two 𝑥. So to find the area of that square, we’ll need to multiply two 𝑥 by itself, two 𝑥 squared. 13𝑥 times six 𝑥 equals 78𝑥 squared. Bring down our subtraction; two 𝑥 squared equals four 𝑥 squared.
Because 78 is being multiplied by 𝑥 squared and four is also being multiplied by 𝑥 squared, these are like terms. Like terms can be added together or in this case subtracted from each other. To combine like terms, you combine their coefficients. 78 minus four equals 74, and then we bring down our variable 𝑥 squared. The expression 74 𝑥 squared would give us the area of the shaded figure.