Video Transcript
Find the area of the shaded region.
In this question, we are asked to find the area of a shaded region in a diagram. We can see that the figure we are given contains two rectangles whose side lengths contain an unknown 𝑥. We can then observe that the area of the shaded region is equal to the area of the inner rectangle subtracted from the area of the outer rectangle. We can then recall that the area of a rectangle is equal to its width multiplied by its length. So the outer rectangle has area two 𝑥 times 𝑥 plus two, and the inner rectangle has area four multiplied by 𝑥. The difference in these expressions gives us the area of the shaded region.
We can simplify this expression for the area by distributing the monomial factor over the binomial. We do this by multiplying each of the terms inside the parentheses by the monomial to obtain two 𝑥 squared plus four 𝑥 minus four 𝑥. We then have that four 𝑥 minus four 𝑥 equals zero. So the shaded region has an area given by two 𝑥 squared.
