The length of the rectangle is 8 cm longer than the side of the square and the width

The length of the rectangle is 8 cm longer than the side of the square and the width is 8 cm less. Which of the figures has a larger area and by how much?

The length of the rectangle is 8 cm longer than the side of the square and the width is 8 cm less. Which of the figures has a larger area and by how much?
Let us assume that the side of the square is a. The length of the rectangle means it will be a + 8, and the width a-8. The sides of the rectangle will be a + 8 and a-8. Now we will find their areas: Sкв the area of the square a ^ 2 (a in the square), and Sпр the area of the rectangle (a + 8) * (a-8); Spr = (a + 8) * (a-8) = a ^ 2 + 8 * a-8 * a-64 = a ^ 2-64; It is immediately clear that Sпр = a ^ 2-64 is less than Sкв = a ^ 2 by 64.
Answer: Sq is 64 more than Spr.